This character would be nothing more than The Ditz, except they have one area of expertise in which no one can beat them. When that skill or talent is needed, they suddenly switch gears from airheadedness to hyper-competency. Sometimes they don't even know that they're doing it.
Genius Ditz is closely related to Idiot Savant. An extreme form may border on The Rainman. The main difference between those tropes and the Genius Ditz is that the Genius Ditz is merely stupid outside his field of expertise while the Idiot Savant and The Rainman are implied to have genuine mental disorders.
Such a character who is well respected may become a Bunny-Ears Lawyer. Opposite of the Modern Major General, who appears to have specialised incompetence. Contrast with Cloudcuckoolander. Compare Too Dumb to Fool. Compare and Contrast Ditzy Genius.
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Anime & Manga
Mazinger Z: Kouji Kabuto is mostly infamous by being an Idiot Hero (mainly due to the anime series, since in the original manga he was more careful, more tactful, and believe it or not, less sexist). But unlike many similar hot-heads, he is actually exceptionally bright when he allows himself to think things through. This is demonstrated both in the Mazinger Z series, when at least twice he had to completely disable mechanical beasts with hostages inside (one of them being Sayaka's disabled cousin, Yuri); and in the UFO Robo Grendizer series, where he builds his flying saucer all by himself and later develops the Cyclone Beam. He is also an excellent shot (demonstrated in the Mazinkaiser VS Ankoku Daishogun movie when he shoots Archduke Gorgon in both his tiger head and human head with one shot). It should be noted that Koji is sent to America in Great Mazinger to study, so he can become a scientist since Kenzo, Koji's father mentions that he has the scientist blood of the Kabuto family inside him. So, it’s pretty much hereditary.
Mihoshi Kiramitsu from some of the various continuities. (Talent: Several, actually. Full eidetic memory, outrageous luck and the ability to get into places where she shouldn't — or couldn't possibly — be.) In the OVA, however, she tends more toward Bunny-Ears Lawyer. It's lightly implied in many of the continuities that Mihoshi used to be a genius cop, but she got so overstressed that she had a mental breakdown — thus becoming the way she is now and that the moments of hypercompetence are actually remnants of her former self. Word of God also has it that she's the great-great-great-great granddaughter of Washuu... As in the 8th-dimensional goddess, greatest scientist in the universe, Washuu. Part of her ridiculous luck/genius moments/otherworldly skill is some fraction of that sort-of-divine spark emerging within her.
Shima Katase from Stellvia of the Universe, directed and produced by the same people as Nadesico. (Talent: Genius programmer.) Granted, she is not as ditzy as Yurika...
Mutsumi Otohime from Love Hina is a classic example. When studying for her exams, she aces the practice tests, but in the actual exam she fails because she forgot to write her name on the paper, or how she once fainted before the test started.She also notices things the other characters don’t even pick up on, such as When the girls go to rescue Keitaro the island they where on was on the other side of the international date line she was the only one who knew and thus Keitaro’s exam was sent back in time for him to make it in to Tokyo U at last. She knew the others at the Hinata inn's names even though Keitaro and Naru didn't tell her. Tama did. But she conscientiously kept that on the down low at first. Mutsumi is the only one that could instantly tell Su’s brother (cousin) was not the real Keitaro and vise versa...etc etc. Mutsumi becomes somewhat less ditzy but continues to affect ditziness in order to keep people around her guessing. (Talents:Super attentiveness, Genius levels of intelligence, sharp keen senses, good luck, calm and peaceful hearted rational.)
Most of the characters from Mahou Tsukaitai are Genius Ditzes of one type or another. The main character is useless at everything except her magic, which is superpowerful, and the white-haired girl is literally a complete ditz until she does magic, at which she's better than anyone else, except that she makes things spin when she affects them with magic.
Ed from Cowboy Bebop is a genius hacker who otherwise has trouble even communicating in normal speech, and often seems prone to wander off chasing the most recent interesting thing that crossed her line of vision. In one episode it was revealed she is also good at chess, she is also quite dexterous.
Yomiko and, to a greater degree, the Paper Sisters of Read or Die fall into this category, generally acting as lazy, incompetent, and clumsy bibliophile Pretty Freeloaders... that is, until it's time to sharpen their index cards and head out in their true capacities as paper-wielding super-spies.
Ryuichi Sakuma from Gravitation in his spare time is a hyperactive, pun-loving kid adult who makes the Keet-like Shuichi look subdued, but on stage proves why he became Japan's most famous singer. In the manga, though, he displays insight and quick thinking even when in "ditzy" mode, which makes him more of a Bunny-Ears Lawyer in original canon.
Bleach: Action Girl Mashiro Kuna acts like a Woman Child and dresses up like a Kamen Riderfangirl, but she can keep her Hollow mask on for hours outside of battle. And was a Vice-Captain in the Gotei 13 before she became a Visored.
Gourry Gabriev is a brilliantly talented swordsman who is otherwise about as sharp as a bag of wet sponges. In the books he's just Obfuscating Stupidity and finds great fun in irritating famously short-tempered Lina. Gourry's problem is often implied to be some rather skewed priorities more than anything else (though he obviously has some memory issues, too): the two most important things to him are fighting and food, and if it doesn't have to do with one or the other he isn't likely to remember it. Thus, he might forget the names of some of his closest friends and frequent traveling companions, but he knows right away Lina's lying when she tries to convince him that he promised to give her his prized Sword of Light and forgot about it because there's no way he'd promise that in the first place. He is also shown to be surprisingly perceptive; if you pay close attention, he's usually the first to notice when something is amiss. Hence, he picked up on Xellos' true nature early on but didn't say anything because he thought it was too obvious.
Naga and Martina are very inventive magic users who are crippled by being almost too crazyto live and exist as lowly Goldfish Poop Gang. Naga developed several interesting spells, but is so self-absorbed she barely manages not to walk into walls. Martina uses magic via worshipping of a Monster she admits she made up herself and it somehow works — but who living in a visual range of sanity would even try such a thing? Which she combines with being petty, clumsy and falling for anyone she deems at least 2/3 ofTall, Dark and Handsome (until she met the real thing).
Inoue Miyako is pretty handy with computers — and for that matter, anything technological — but tends to be a fiery Genki Girl otherwise.
Kudou Taiki in Digimon Xros Wars. He not only seems, he IS an idiot. However, his strategic prowess is simply amazing, from distracting a foe by calling the wrong attack, to resist the temptation to attack from the front like any other hot blooded hero would do and instead taking an enemy vessel and blow the unsuspecting others to smithereens. AND HE'S TWELVE YEARS OLD.
A common Fanon view regarding Ranma Saotome, titular character of Ranma ˝, but it doesn't really match canon. While he doesn't seem to care that much about schoolwork, he is implied in both canons to do at least average, he has a wide amount of eclectic knowledge and can usually be counted on to know at least something helpful about just about anything, and is pretty much an expert at improvisation and tactical thinking. Pretty much everyone he knows is impressed at his skill at spotting weaknesses in an opponent's fighting style, revising techniques (or applications of techniques), and otherwise finding a way to come out on top. The one skill he does seem to lack in is social skills, but that is justifiable partially due to Ranma being a very private person (even his "real" girlfriend, Akane Tendo, doesn't know much about him or have any insight into his thoughts) and partially due to the Muggles he interacts with naturally being scared off. Between the switching sexes with cold/hot water deal, the dangerously indiscriminate inhumanly skilled rivals, the almost-as-bad would-be love interests, the two Old Masters (one of whom is a Dirty Old Man who literally lives to grope girls and steal their underthings), and the general frickin' strangeness that seems to seek him out like flies chasing honey, it's no wonder that they consider him one of the school freaks.
Son Goku of Dragon Ball is so naive he didn't know the difference between boys and girls until he was 12, even miscounted his own age at one point. However, his brilliance is found in fighting, first and foremost. He learned how to fire his own Kamehameha wave simply by watching Muten Roshi do it, despite the fact he took fifty years developing it, not only took it as his signature move but created variations and enhancements of the move Roshi couldn't have possibly foreseen, proclaiming him to be a "genius". Also, learning the Kaio-ken and the Genki Dama not only took him less than nine months to learn, but even though with the former he's not supposed to multiply it by even beyond twice, he found a way to push it to times twenty, and the latter he found a way to gather energy from nearby planets and collect it. He even discovered the weaknesses behind his own Super Saiyan form just by using it once, and find an effective way to use it. Not to mention that he learned the After Image technique after seeing it only once and even tricked his master with it. He also used the Solar Flare successfully against its own creator after seeing it used only twice. He also so savvy in battle that he often outsmart fighters who are much more intelligent than him.
Athena from ARIA is regarded as a highly respectable undine and is even known as one of the three "Water Faeries" of Neo Venezia — which is also helped by her singing abilities. Still she is prone to extremely ditzy behavior, sometimes being spaced out so much that she comes dangerously close to being a Cloudcuckoolander.
Natsuhiko Taki from Eyeshield 21 is an utter moron, plain and simple; He doesn't even know his times tables. But if a question is asked in terms of American football, no matter how complicated, he'll always answer it correctly in seconds.
Tamaki Suoh in Ouran High School Host Club — crazy idiot, but can play the piano better than anyone. He also demonstrates amazing interpersonal insight from time to time, making his huge success as a host more than an Informed Ability. He's ranked second for his grade, right below Kyouya. And he apparently doesn't even study.
Azumanga Daioh's Osaka isn't the sharpest knife in the drawer but don't challenge her to games involving marine biology or obscure kanji.
Yui from K-On!, especially after Azusa arrives. Best example: Yui doesn't know what a guitar tuner is; she's only able to tune her guitar because she has perfect pitch. Which gets even worse, because she doesn't know what perfect pitch is...
Koga Haruka from the manga/anime H2. She can be a bit silly at times but her true ditziness is only her clumsiness; she even carries bandages around because she keeps hurting herself.
Kazuma Azuma from Yakitate!! Japan is skilled in three things: Bread-making, rice, and... math, for some reason.
Misa Amane. Boy crazy, childish, bubbly... and a devious, intelligent mass murderer. It took the world's best detective (assisted by forensics laboratories) to track down the extremely unlikely evidence that revealed her identity as the Second Kira. In this regard, she only looks like a ditz next to Light, and because her obsession with him blinds her to the rest of the world.
L himself could also count as a Genius Ditz. He's the world's three greatest detective s. He also is constantly eating cake, sitting oddly, and being completely oblivious to conventional manners.
The version of Professor Moriarty from Meitantei Holmes (US name Sherlock Hound) is capable of devising brilliant criminal schemes and performing remarkable feats of engineering, but has trouble with common-sense issues like checking the pressure gauge on a steam press so it doesn't explode, ensuring that the river he's using for a Hostage for MacGuffin exchange is actually deep enough to be any sort of obstacle, or not following a small child out onto an aircraft wing that's made out of paper and can't possibly support his weight.
Sheska from Fullmetal Alchemist is clumsy, daydreams, and can copy a book word for word for weeks or even months after she has read it. Just give her the book title/description, it can be anything with words, including records. This is how she lands the job recreating all the character files burned in the Central Library while being overseen by Hughes. She can also remember all the facts in said books as well at the drop of a hat!
Patti in Soul Eater. Has martial arts skills to outdo most of her class, and is so enthusiastically destructive at a firing range that Sid gives up trying to teach her anything. Puts this to good use when acting as Liz's meister. The series is full of this sort of oddly talented character.
Hayate the Combat Butler: Isumi Saginomiya. Full stop. She can barely figure out how to open her cellphone, and has attempted to travel to Nagi's mansion on several occasions. Unfortunately, having zero (nay, having less than zero) sense of direction, she often finds herself on a train to Rio de Janeiro or some frozen wasteland in the middle of nowhere. The genius part comes in when confronted with something supernatural. She swiftly banishes even the most powerful of demons with incredible grace. During the Athens arc, she turned her No Sense of Direction into a Big Damn Heroes moment, while also subverting the 'defeating any powerful demon' clause.
One Piece: Tony Tony Chopper is an excellent doctor, and aside from being an anthropomorphic reindeer, would fit in at just about any hospital in the world. But if it doesn't have to do with medicine, he's extremely childish and naive enough to believe Usopp's stories. Luffy himself is in the same childishness and naivete ballpark, but his talent is pure ass-kicking (and figuring out new applications of his Rubber Man powers).
Where isNaruto in all this? He may be your usual Idiot Hero but when in battle, he shows his ingenious talent at formulating tactics. His mother, Kushina is also implied to be this as she admitted that her Ninjutsu grades in the Academy sucked, but she is apparently talented and knowledgeable in the art of Fuuinjutsu (Sealing Techniques) as it is her clan's specialty and apparently taught Minato the Uzumaki-Fuuinjutsu style which played a huge part in him becoming a legend.
Saiyuki might have the most genuinely ditzy of any ditz who ever did ditz in KoumyouSanzo. He acts at times exactly like a valley girl, sleeps through his classes when he's in training, uses slang words he is FAR too old for, seems to misunderstand questions and situations a lot... and is also the youngest Sanzo priest ever before Ukoku and Genjo come along, was a mentor figure to both of them, and also the only person both of them actually acknowledge as worthy of respect, was so powerful they bequeathed him two sutras, something never before done, and generally is one of the biggest badasses in the series, albeit one who died before it started. Is an interesting case in that his Genius is not really divorced from his Ditziness, and a lot of his insights come from that aspect of himself.
Lloyd from Code Geass is an airhead who doesn't seem to care about politics, the rebellion, Zero, justice, or basically anything that is not mechanical. Yet, he is a genius scientist specialized in building the most powerful war machines in the world.
Deadpool probably counts as one. Sure, he's certifiably insane, completely unpredictable, constantly breaks the fourth wall and never ever ever stops talking — ever — but when it comes to fighting, shooting, stabbing and generally causing mayhem, he's one of the best in the whole Marvel Universe. Suffice it to say that Deadpool is really good at his job as a mercenary. He once detected seventeen weaknesses in Shatterstar's fighting techniques just from watching him practice for a few minutes. Shatterstar is one of the best swordsmen in the entire Marvel Universe, and quite skilled at all other forms of close-range combat to boot.
Several Donald Duck stories would have the titular duck discovering an previously unexpressed aptitude at some obscure field, like counting objects or instrument playing.
Modesty Blaise's lover Dr Pennyfeather, a bungling but surprisingly efficient doctor.
In Doom Patrol, Flash Forward is The Smart Guy and a Deadpan Snarker who often shows a greater capacity for lateral or existential thought than his teammates. He's also a poor kid from rural Alabama who dropped out of school in the 7th grade.
Miss Martian from the Teen Titans comic has pulled some rather impressive stunts like disguising herself to infiltrate a underground super fight league to free a bunch of trapped superheroes and working with a resistance cell in Final Crisis. She also threw a pie in Ravagers face and cried when Rose yelled at her.
Every once in a while Harley Quinn will remind you that she is a certified psychologist. Interestingly, she seems to have been ditzy even beforegoing insane, though. For a long time, writers went back and forth as to whether she truly earned her degree or whether she cheated her way through school to get it, until her own series, where they eventually settled on the former.
Dungeon Keeper Ami has Mukrezar, an example with a serious bloodthirsty streak. Unlike most examples, however, he dosen't appear to have any real mental impairment, aside from his general maddness. Most of it is simply his willingness to try ridiculous schemes, despite, or perhaps because of how unlikely they are to succeed. But he's a terrible cook.
Lockhart in Oh God Not Again is interpreted like this. While he's still incompetent as a teacher, Harry admits he's a genius when it comes to anything dealing with the media.
Mr. Ping in Kung Fu Panda would in most senses be only The Ditz — as Word of God puts it, "he's got a tiny little head, and there's nothing in it except noodles. And love for Po." However, not only is his knowledge of noodles and cooking in general something he is obviously very skilled at, since he teaches Po everything he knows and the Furious Five (almost) unanimously declare the panda's cooking sensational, but the end credits reveal he has another hidden talent: to judge by Shifu's horrified expression, Mr. Ping is apparently a stellar player of Mahjong.
Linguini from Disney/Pixar's Ratatouille is shown as gangly, clumsy, dorky, fluent in Buffy Speak, and utterly useless at cooking, ruining a soup so badly he caused himself to throw up upon tasting. Then he discovers that it's legal to wait orders on rollerskates, and becomes little short of a Super Waiter.
Barbie in Toy Story 3, aside from being more of an Action Girl than you might expect, seems to have a bit of a knack for political science when the heroes confront the Big Bad.
Ragetti is illiterate and lacking in common sense, but behind that wooden eye lies the brain of a philosopher, scholar, and man who knows the original Scandinavian pronunciation of "Krakan". He's also the one who figures out how to free Calypso.
Will was one of these in the first movie: though not a complete moron, he's pretty slow on the take and in way over his head. Until it's time for a sword fight, in which case, your arse is grass.
Elle Woods of Legally Blonde maintained a 4.0 GPA (albeit as a fashion major), frequently came up with rather "creative" events for her sorority, and got a 179 on her LSATs. And while still a law student, she literally wore Bunny Ears to what she'd been told was a costume party. Her encyclopedic knowledge of hair care saved her first client from death. (Based on a True Story or something; the author of the original semi-autobiographical book admitted she picked Stanford Law School [the film relocated the story to Harvard] because it was close to her favorite national mall.) No matter what your major is, you still have to take math, science, history and English classes unless you are at a tech school or attending either Amherst or Brown. Smart and shallow are not mutually exclusive.
Brick turns out to be one in Wake Up Ron Burgundy (a 'film' made from deleted scenes in Anchorman).
Ron Burgundy: All right, gang, it's real simple. Just like when we were back together in 'Nam in '64. I'll take the point...
Brick: Stand down, Corporal Burgundy. I'm running this show now. Affirmative, a-ffir-ma-tive? - Affirmative. I'll take point. Champ, right flank. Gator Dirty Teacup. We will fan out, to a cobra double-helix formation. If we encounter any hostiles, silent throat cuts only. On my... mark.
Ron Burgundy: Looks like the captain's back.
Cleverly played with in the film Fool's Gold with the character of dim heiress Gemma. The female lead has been (impatiently) coaching Gemma she is smarter than she acts, so when Gemma has a sudden brainwave as the heroes return to their yacht the audience naturally expects some amazing insight that will find the treasure they have been searching for while confirming Gemma is more than just an airhead. Actually it turns out to be that Gemma has only just realized that the name of her father's ship ('The Precious Gem') is, get this, similar to her name.
The 2008 movie version of Get Smart casts Maxwell Smart as something like this: whilst he's notably clumsy and overconfident as a field agent, his abilities as an intelligence analyst are noted by many characters to be the finest in the agency. They also come in handy in the field; his in-depth understanding of and empathy with a Punch Clock Villain enables Smart to give him some relationship advice — in return, the henchman spares Max and 99 and later tips Max off about a bomb in Los Angeles. Smart is also presented as being surprisingly cunning, resourceful and a crack shot, proving his usefulness to Agent 99.
Rebecca Bloomwood in the film version of Confessions of a Shopaholic, who is genuinely ditzy but (to her own surprise) proves brilliant at explaining prudent finance to lay people through shopping analogies.
In the post-credits scene in Women in Trouble, Holly Rocket turns out to be pretty good at trigonometry. It's not a perfect example of this trope, since the question she answers is really just a pretty conventional high school math problem, but in the context, it works.
Lorelei Lee from Gentlemen Prefer Blondes is the stereotypical Dumb Blonde (she is played by Marilyn Monroe in the movie version) but she's an expert on diamonds and is able to come up with plenty of well-thought out plans to solve some of the problems she gets herself into. She also manages to convince her fiancee's father exactly why his son should marry her, stunning him with her knowledge and then saying that his son loves her for her brains.
In Georgette Heyer's novel Cotillion, Freddy Standen is generally (if fondly) regarded as a complete idiot by most of his family. However, he has impeccable manners and his shrewd knowledge of social niceties make him extremely competent at dealing with the situations the heroine finds herself in. As she notes, Freddy may not have brains, but he does have address, which is far more useful.
Fred Colon of the Ankh-Morpork City Watch, a long-time copper (who is in fact at the age he should have retired but has decided he doesn't want to) who is not very intelligent, but has peerless instincts as a Watchman.
Brutha from Small Gods can't read or write, but has a perfect memory.
Stanley from Going Postal appears to be Raised by Wolves (by peas, actually) but has an encyclopaedic knowledge of pins, and later, postage stamps.
Also in Monstrous Regiment, Lieutenant Blouse repeatedly shows himself to be a useless, incompetent officer who exasperates the experienced Sergeant Jackrum in every scene, yet astounds William De Worde by extrapolating the mechanics of the Clacks system without even seeing them up close.
Mr. Tulip in The Truth is a hulking bruiser who could probably be outsmarted by Detritus on a warm day. He's so dumb, in fact, that his efforts to cultivate a drug habit have resulted in him snorting baking soda, washing powder, powdered chalk, etc. and never knowing the difference. He doesn't even swear properly; he just drops an "-ing" three times in the average sentence, and it's not a euphemism for anything. Show the man a work of art, however, and you'll suddenly have a giant, slurry-mouthed, red-nostriled expert on your hands.
Owlswick Jenkins in Making Money is clearly suffering from some sort of mental illness, including paranoid delusions of being followed by "Them", and so removed from reality that he he can't even comprehend the illegality of forging government stamps. But put him in front of a canvas and hand him some paints and he'll produce artwork so intricate that it's impossible to forge. Igor tries to fix him by transferring his insanity into a turnip, but he loses his artistic abilities in the process and is forced to switch back.
Leonard of Quirm shows flashes of this in his appearances. He's not so much "pure ditz" as he is absent minded and unbelievably naive, but he's also probably the most brilliant, and potentially dangerous, inventor on the Disc.
Neville Longbottom can't seem to cast even the simplest spell without a critical fumble... until he discovers that he's crazy skilled at Herbology. And then Took a Level in Badass around the 5th book.
Professor Sybill Trelawney is both this trope and its inverse: she is apparently utterly incompetent at Divination, her own field of study. However, upon occasion, she is capable of oracular predictions about the future, which, due to happening in a trance, she knows nothing about, and refuses to believe in when she is told what it was that she predicted. While her normal predictions are about as reliable as a take-out Chinese restaurant's fortune cookies, anything she says in her trances will come true.
Freddy Arbuthnot from the Lord Peter Wimsey novels is a classic Genius Ditz, whose talent is finance. Lord Peter himself comes across as this, though that is explicitly stated to be a coping strategy for the post-traumatic stress he acquired in the Great War.
Julia Larwood of Sarah Caudwell's Hilary Tamar mysteries is presented as a highly skilled tax barrister who, apart from regularly getting lost in the city she lives in, completely forgets to pay her own taxes.
Enrique Borgos in Lois McMaster Bujold's ''A Civil Campaign''. Brilliant at biochemistry, but the man lacks knowledge of economics, social interaction, plumbing, personal hygiene, and can barely tie his own shoes.
Dr. Stephen Maturin, from Patrick O'Brien's Aubrey-Maturin series of naval history novels. Although a well respected physician and natural philosopher, after having been at sea for nearly 20 years he can barely row a boat, and still doesn't understand basic nautical terminology.
Jack Aubrey himself is an even better example. He is a highly skilled sailor and capable personal combatant. He has also become so good at the mathematics and astronomy needed to navigate he has come to the attention of the Royal Society, he builds his own telescopes, and is an accomplished violinist. He is also dreadful at languages, dispenses wisdoms like "they have made their cake, and must now lie in it" and firmly believes the sons of Noah were named Cain, Abel and Moses.
Georgette "Buffy" Messonier in Mira Grant's Feed is a dreamy space case who makes her living writing zombie romance and poetry, but her technological genius is eclipsed only by her paranoia — she managed to successfully bug pretty much every government office she ever set foot in, and given that she was part of news team embedded with Senator Ryman's presidential campaign, she spent time in a lot of Super Secret Locations. Some of her public persona may have been Obfuscating Stupidity, but she was still pretty ditzy.
Paul Dekker, from C.J.Cherryh's Heavy Time and Hellburner has basically no sense of time, routinely forgetting which year it is and vividly hallucinating past traumatic events. The other side of the coin is his ability to hyperfocus (concentrating very deeply, improving his reaction times) which allows him to fly space fighters moving at significant fractions of lightspeed.
In L. Jagi Lamplighter's Prospero Regained, Mephisto, so crazy as to earn the nickname "Harebrain" nevertheless manages to persuade his brothers and sisters to let him lead them — and then does it.
Mothflight from Warrior Cats. While she spaces out a lot, leading to some near-death situations, she's an expert with herbs and healing.
Simona Ahrnstedt gives us Sofia Löwenström in her debut novel Överenskommelser. While you can't call her stupid, she still comes across as a fragile pretty-face, who never could manage in the world on her own. But at least she's really good at playing the piano (which ironically seems to be the only thing, that her otherwise super-competent cousin Beatrice can't do).
Live Action TV
Cordelia in Buffy the Vampire Slayer is often vacuous, insensitive and viewed as an airhead by others but she was declared "a brain" by Xander after he saw her SAT scores, she got into numerous Ivy League Universities and she was in the top 10% of her year at school. Her insensitive comments often portray that she is a shrewd observer of human nature.
In Merlin, the title character is a servant who has trouble cleaning his own room, let alone Arthur's, manages to trip over nearly anything you put in front of him, is a horrible liar (about the little things), gets things thrown at him all the time by the prince, doesn't respect royalty and gets put in the stocks all the time, can barely hold his liquor, rarely varies between the social extremes of over-affectionate and sarcastically aggressive, has a weird penchant for awkward situations... and also happens to be the most powerful, badass warlock the world has ever known.
Herb Tarlek, the unlikable, tasteless ad salesman from WKRP in Cincinnati was considered a stooge by his coworkers because of his abrasive personality and atrocious wardrobe. However when they "fixed" him in one episode by changing his look, it became apparent that the low rent clientele of such a low-rated radio station no longer felt welcomed by Herb's new "upscale" persona. As horrible as he was, he was perfect for the job he had.
Ricky in the Canadian comedy series Trailer Park Boys is an absolute moron most of the time, but whenever he and best friend Julian are at risk of being arrested by the police, he suddenly becomes a tactical genius, able to generate fake evidence and alibis that get them off the hook 99% of the time. Nevertheless, almost every season ends with the pair being arrested and sent to jail. Ricky's also an expert when it comes to growing marijuana and converting it to hashish. He and Julian make an effective team when it comes to dealing drugs — Julian handles the business side of the operation, while Ricky grows and harvests the dope crop.
Troy Barnes may be dumb in the most lovable way, but he's still pretty dumb; except for his incredible natural talent as a repairman. He even gets coerced into joining the cult-like Air Conditioning Repair Annex because of his abilities.
Pierce Hawthorne is a ditz through and through, but is also hinted to be a competent businessman and a skilled orator.
Waldo of Family Matters. After spending a couple seasons as The Ditz bordering on the Cloudcuckoolander, he surprises everyone when he takes a home economics course and proves a natural genius as a chef, to such an extent that in one episode he reveals he was trading recipes with Wolfgang Puck. His mom is a lousy cook, so he had to fend for himself.
Rom, from Star Trek: Deep Space Nine, appears to be a total idiot for much of the time — until he reveals a hidden, and borderline savant-like, talent for engineering. (A field Ferengi have little respect for.) His son Nog (introduced as a petty thief with no respect for women or education) proves to have some of his uncle's business acumen, a knack for engineering, and in one potential future becomes a respected Starfleet captain. Most notably (although it also doubles as Characterization Marches On) Rom is described early on as "an idiot" even by Constable Odo, who has a Sherlock Holmes level of attention to detail.
Fargo North, Decoder in The Electric Company is clumsy, egotistical, and obsessed with sandwiches. However, as his name implies, he is a great decoder... well, actually, sometimes he isn't even good at that. Sometimes he forgets where the period goes, for example (this is deliberately done so that the kids at home have a chance to figure it out themselves). Nevertheless, the rest of the characters always turn to him for all their decoding needs.
Michael Scott, from the American version of The Office is childish, selfish, egotistical, deeply insecure and lonely, and an all around buffoon with no managerial skills whatsoever. He also demonstrates on occasion that he is a superb salesman who is roundly beloved by his clients, which is what got him promoted in the first place. (David Brent, his counterpart in the original UK series, lacks any such redeeming features). He also occasionally demonstrates a certain cunning streak, such as when he tricked Dwight (who had been gunning for his job) into thinking he had been promoted in order to tear it away from him in a manner which would ensure that he would never try such a thing again and when he bluffed David Wallace into buying out his worthless and bankrupt company by hiring back himself, Pam and Ryan.
Carter from Hogan's Heroes is enthusiastic but generally oblivious and he tends to get teased for his cluelessness — until they need something blown up. Or Hitler impersonated. He's scarily good at impersonating angry German officers of various calibers, despite his puppy-esque normal demeanor.
The (radio) newsreader in In The Red is invariably stoned and away with the fairies — right up to the second she goes on air, when she suddenly turns completely sane and professional.
Shawn Spencer of Psych tends to be immature and goofy and annoys the heck out of everyone he works with... but they put up with him because underneath all the psychic hoopla, his Hyper Awareness makes him a brilliant detective.
Likewise, Adrian Monk of Monk is normally unable to function in society due to his severe obsessive-compulsive disorder and fear of just about everything. However, once he sets foot in a crime scene, he can almost instantly solve the crime with the smallest or most overlooked pieces of evidence.
Monk's brother exhibits similar qualities: He has an extreme case of agoraphobia that prevents him from (nearly) ever leaving his house (as well as a related phobia that prevents him from entering the study of their father), but is evidently a highly skilled writer of technical manuals.
Lord John Marbury from The West Wing is a specialist on India and Pakistan who is prone to great insight on the subject. Too bad that the rest of the time, he's a pompous Cloud Cuckoo Landerwho can't even keep Leo's name straight. Then again, this may be more Obfuscating Stupidity / Obfuscating Insanity, coupled with a mischievous desire to needle Leo (he also frequently claims to have mistaken Leo for the White House butler) than anything that belongs on this page. His persona does seem to radically shift when he gets serious, including getting people's names right, making it seem at least partly a strategy.
Joey from Friends is dim, shallow and a fairly bad actor, but he has an amazing talent to attract girls. It helps that he's blandly pretty and can be quite earnest. He also once memorized everything from an encyclopedia volume (the one with the words starting with "V") and he was the first one from the gang to deduce that Monica and Chandler are hooking up.
Mr. Bean from Mr. Bean on some occasions but most of the time he comes across as just The Ditz. Mr. Bean's Diary includes the character's school certificate on which, among others, the following marks are given:
Chemistry — 53% — He is inventive. As a result, form. SB is lucky to be alive.
Physics — 65% — Very encouraging. A boy died when co-operating with his lie-detector experiment, as you know, but nevertheless the exam results are excellent.
Geography — 54% — A surprisingly good result considering he only succeeded in finding the classroom twice this term.
Art — 58% — He draws well, but has difficulty with nudes (looking at them).
Mathematics — 94% — An obnoxious, self-satisfied, self-centred, shabby, dribbling, bone-idle, toadying cow-put of a pupil; his most revolting quality being that he is quite, quite brilliant.
Kramer on Seinfeld is a prime example of the character whose life is a complete shambles (no job, no source of income, no sense of stability or direction, and no clue how or if his situation is ever going to change) and who would seem to be a perfect male incarnation of The Ditz (as he doesn't really appear to be concerned about any of the above), were it not for the fact that, as at least one major character has remarked, his "...whole life is a fantasy camp. People should plunk down $2000 to live like him for a week. Sleep, do nothing, fall ass-backwards into money, mooch food off your neighbors and have sex without dating... that's a fantasy camp." He might also be considered an example of an Idiot Savant.
Donna Noble was constantly self-defeating at her own brilliance, and yet her training as a temp has got her out more than one scrape.
Jo Grant. She's a Plucky, skilled escapologist who once managed to dig her way out of her cell with a spoon. She's also thicker than a plank. She's also possibly the only character in the entire series (at least out of the John Pertwee era) to resist being hypnotised by The Master through sheer willpower alone. Jo can be said to have "matured" over the course of the series, starting off as this before gradually getting smarter.
Zoe Heriot, who was a whiz at physics—but didn't know her history (c.f. The Wheel in Space part 6, "The Stolen Earth") and had a hard time disregarding what she saw when she needed to (c.f. The Mind Robber).
Kelly Bundy from Married... with Children has, on a couple of occasions, shown herself to have a few shining moments of competence. Some instances include figuring out the correct way to assemble a work desk that her father and neighbor had worked on for a day in a matter of seconds, and piercing an apple off the head of her brother with a bow and arrow when angered by her competitor. She was also capable of learning a huge amount of sports trivia in 48 hours. After several seasons of Flanderization where she became more and more stupid, there was a flashback showing Kelly as a bright, polite, bookish girl... Until Al slammed on the brakes and she hit her head on the back of the seat in front of her, and when asked if she was okay only responded with "Shiny, shiny shoes!" Cue Oh Crap look from the parents.
Maddie: This is insane! How can you be so good at chess!
London: You just stink at chess.
Maddie: But I'm the smart one!
London: You're Maddie, the smart one who stinks at chess.
Gem and Gemma from Power Rangers RPM act like 5-year-old psychopaths, but they're geniuses when it comes to advanced physics and technology.
Amber, the intern at Red, White & Blue in Brothers and Sisters. A ditz and fairly excitable, she is a genius when it comes to politics and research.
Super-goofy and clumsy Matthew is an incompetent radio station cub reporter and office boy in NewsRadio, then he got fired during two episodes revealing to have a degree in dentistry (which he detested) and actually finding a job as a highly skilled and competent dentist, only to revert to his usual state after being rehired at his old job.
Junior from My Wife and Kids. He's stupid, but he has proven himself to be smart when necessary, and he's a great cartoonist.
Chumlee from Pawn Stars isn't allowed to handle any money in the store, is referred to as the "village idiot" and only has any useful knowledge in a few specific areas. Yet when it comes those areas, such as tennis shoes and pinball machines, he knows more than everyone else there.
Perceval on Kaamelott can barely form proper sentences but he is a genius at mathematics.
Fletcher from A.N.T. Farm skipped several grades due to his artistic ability, but he thinks snow angels are dead snowmen.
In Survivor's 21st season, Nicaragua, contestant Jud Fabio Birza is revealed to be this. The early episodes show him doing some unbelievably stupid things like getting the fishing hook caught in his thumb, apparently not knowing crabs can pinch, annoying the hell out of other contestants, and asking Kelly B if she can move her prosthetic leg. He revealed later on that while he honestly is kind of this way in real life, he pretty much exaggerated this in the show specifically so people would underestimate him and he could pull a Crouching Moron, Hidden Badass. And boy did it work, as he won the season.
Brittany Pierce may think the square root of four is rainbows, but put the girl on a dance floor and prepare to be blown away. Also, she knows an unbelievable amount about feline diseases. In the season four finale it is revealed that she was admitted to MIT because the doodles she made on the back of a test paper turned out to be a revolutionary new way to look at mathematics.
Lydia Martin and Stiles Stilinski both display signs of this on Teen Wolf. Lydia is a vacant Alpha Bitch, and you wouldn't know it from her fashionable exterior or Jerk Jock boyfriend, but she has a 5.0 GPA and a brilliant scientific mind capable of coming up with self-igniting molotov cocktails using the materials available in a high school chem lab. Stiles talks. A lot. But he also has perfect grades, despite having ADHD severe enough that he wrote an essay detailing the history of male circumcision on his econ midterm. He's an amazing investigator and a brilliant researcher, but no one who just looked at him would tell you he was competent.
Skull from Mighty Morphin' Power Rangers is incredibly stupid/lacking in basic common sense; amongst other things, he's been shown opening a shaken can of soda directly into his face and having a difficult time pronouncing simple words like "fourth". In Power Rangers Zeo, he is revealed to be an incredibly talented, classically-trained pianist. Obviously he's got some smarts in his head, since when he reunites with Bulk at the end of Power Rangers Samurai he arrives in a limo wearing a nice suit.
Parks and Recreation: Andy Dwyer is a loveable ditz (after Season 2) and a not-so-successful musician, but proves to have some Hidden Depths. A perfect example is when he scores a 100 on the written part of his Police Academy exam (a feat that's never happened before), but completely fails his personality test.
Jerry is completely incompetent at his job... but is repeatedly shown to be, outside of his job, a talented artist and musician.
Amber on House of Anubis. While she isn't shown to be very smart overall, she does have many moments of genius and is very skilled at fashion. In the original Dutch version, she's more of an Spoiled Sweet, with some ditzy moments.
In Up The Women Margaret, the wannabe suffragette, is shown to be very clever, writing love letters to Ovid and able to give complex explanations about how electricity works, but she thinks you can get a degree in common sense.
2D of the Gorillaz seems to be something like this, being known to compose beautiful melodies and vivid lyrics, as well as playing multiple instruments professionally, yet failing to wrap his head around... most everything else. Ninety percent of the time he's The Ditz or even Too Dumb to Live, but he'll occasionally say something shockingly deep or philosophical. Some people feel that he's not unintelligent at all, just lazy and eccentric.
A number of rock and pop musicians are very talented despite being unable to read music.
Wigglytuff from Pokémon Mystery Dungeon. Nobody (probably not even himself) ever knows what the hell he's talking about but he is apparently an exploring prodigy.
Both Zell Dincht and Selphie Tilmitt of Final Fantasy VIII come across as being not quite the brightest bulbs, or at least having very short attention spans, but the two of them turn out to be the most technologically savvy characters in the player's party and the designated pilots of the Cool Ship (after the party runs off with it courtesy of Selphie sitting down at the controls: "It just kind of took off!"). Neither of whom are actually unintelligent though. Zell is quite smart and full of information, even having the nickname Mr.-Know-It-All-Zell. All SeeDs must pass rigorous mental and physical training before even being allowed to take the field exams to join the group. They just have a few personality quirks that make them seem like they wouldn't be smart.
Rikku, often clumsy (More so in X-2), can mix items to create deadly weapons. She's also a talented thief. This is almost assuredly obfuscating stupidity, since she's also a skilled mechanic and expresses pretty deep insight into matters on several occasions. Her brother, named oddly 'Brother', is a better example, as he's a total social inept, can barely speak the common language on the planet (granted, he didn't even know it til two years ago, but he's the only bilingual member of his people to have speaking problems), and oftentimes he just misses the point entirely, but he nearly singlehandedly excavated and repaired the airship he's letting you tool around in the second game.
Kang the Mad from Jade Empire is brilliant when it comes to making things fly and explode. In his own words, "The things he flies tend to survive! The things he explodes... not so much." Go to him for anything else, and he's pretty well useless.
Guybrush Threepwood from the Monkey Island series has a fair share of wit and an uncanny ability to craft incredibly convoluted and improbable solutions to almost any problem he is faced with. He's also so ditzy he regularly makes other characters wonder how he can function in everyday life. He can also hold his breath for ten minutes. Which happens to come in handy on many occasions, given the man is a pirate.
Andy from Advance Wars, the only mechanical genius who doesn't know that there's more than one continent! Or what an airport is, apparently. It's more that, for the sake of the tutorial, they superglued an Idiot Ball to him. Unfortunately, perhaps they forgot to take it off him again for the rest of the game.
In Kingdom Hearts, Goofy takes this role. He tends to be one of the more observant of the group, albeit speaking as if it's entirely obvious to everyone else. For example, he's the only one that picks up that Mulan is female at first. He's also oddly philosophical, assuring a worrying Sora that they would end up somewhere, even if The End Of The World disappeared, at the end of the first game.
Alan Probe, the star of Amateur Surgeon. While he's an incredibly talented surgeon capable of performing complicated operations in mere minutes with the simplest of tools (like a pizza cutter and a stapler), and eventually became globally famous and wealthy because of his tremendous skill (with feats such as operating on a Captain Ersatz of Superman and somehow operating on a car that suddenly arrived from the past), the Distant Finale Christmas edition is quick to remind the player that he's still an utter moron. In the sequel, he quickly gets his bearings back despite being a senile 70-year old man. Truly the guy is the world's greatest Back-Alley Doctor. Somewhat averted by Ophelia Payne of the third game, who is the Only Sane Man.
Touka of Utawarerumono is apparently an incredibly competent fighter who can run rings around Oboro and Kouro. She's also a rather goofy airhead who's even denser than Hakuoro and a little too eager to be a bodyguard.
Fire Emblem has Mia, an extreme Genki Girl who's so oblivious that she sincerely believes that a sickly White Magician Guy is destined to be her rival and challenges him to duels on the spot. However, she's very talented with a sword, both in gameplay and in story, as she's allowed to stay with the hero's personal team permanently after the end of the story, and was one of the few teammates to be directly praised by him in the sequel.
Utsuho Reiuji of the Touhou games fits this trope, especially in the fighting game Touhou Hisoutensoku. She's a literal birdbrain (a hell raven) who seems to forget what she was thinking after a few seconds and acts like a total airhead, yet she seems to have a vast knowledge of nuclear physics. She's been doing an excellent job of keeping the nuclear reactor that the Moriya shrine has set up from exploding, at least.
Ellis, of Left 4 Dead 2 fame. He acts like a borderline Cloudcuckoolander and never stops talking, but he's hinted to be the smartest Survivor. Ellis is most often the one to come up with the plan in Dead Center to use the stock car as their escape vehicle, then shows that he is familiar with this type of thing by mentioning that they don't fill up the tanks at car shows, so they need to find gas before they go. This is along with the same campaign, occasionally, Ellis will mention that when this whole thing started he had built an armored car, which he claimed was 99% zombie proof. (the other 1% tore it all to shit though.) While this may not make him the smartest, it does fit the trope.
Coco Bandicoot of the Crash Bandicoot series went in a similar manner to Tails, albeit in an opposite evolution, being an advanced technowiz, but evolving into a ditzy Bratty Half-Pint.
Sandal, from Dragon Age: Origins, bordering on savant. He barely talks (only saying "enchantment"), and mostly just stands around looking dopey, but he's a highly skilled enchanter. Also, at one point, he and his father get attacked. When you arrive on the scene, every mook around him is dead, and when you ask him what happened, he just says "Enchantment!". And again in Dragon Age II, during the Deep Roads expedition, Sandal's adoptive father notices he's missing and asks Hawke to find him. Upon locating the boy, the party sees a bunch of dead darkspawn, including a frozen ogre, with Sandal looking at Hawke innocently.
Hawke: I'd really like to know how you managed to kill all of them?
Hawke: *Points to the Ogre* And how did you do that?
Sandal: NOT enchantment!
Dekar from Lufia II and its remake Curse of the Sinistrals. He claims to be the greatest warrior in the world, and may just be correct despite being a Badass Normal (in the original, anyway). But when a defeated villain promises to have a "special gift" in store for the next time they meet, Dekar asks for a new coat. When not being Crazy Awesome or crazy stupid (or both), however, he can be surprisingly insightful about things such as relationships and the importance of backing up confidence with genuine strength.
Sheegor from Psychonauts is a grown woman who acts and sounds like a little girl most of the time, but apparently is an expert on neurology, since Sasha says that recranializing adults is extremely difficult without surgery. This is probably why Dr. Lobotoenslaved her.
Chaz of Phantasy Star IV. Pretty much anything technical needs to be explained to him and he's absolutely hopeless when it comes to grasping how Algo's technology works, but when it comes to people and emotions, he's quicker on the draw than anyone else in the group. His ability to draw parallels and understand the situations of others is actually a major plot point later on.
Mass Effect 3 reveals that Conrad Verner, a recurring character who tries to emulate Shepard without success and will get himself killed stupidly if dealt with in an incorrect fashion actually has a doctorate in xenoscience and wrote a dissertation on dark energy.
While Nanashi in Duel Savior Destiny is very ditzy indeed, she shows surprising aptitude for herbalism, alchemy, magic and even direct fighting when she manages to beat first Lily and then Taiga in straight duels essentially unharmed.
Emilia Percival of Phantasy Star Universe is incapable of fighting (Or so the character says). She turns out to be one of the smartest characters in the series at seventeen
The Think Tank of the Fallout: New Vegas add-on "Old World Blues" are drug-addicted, disembodied brains who have long since forgotten the most basic facts of humanity (they mistake your fingers for penises). They are also the most brilliant minds of the pre-war world, responsible for game-breaking technologies and many of the Mojave's most horrifying mutant creatures. A good portion of New Vegas' DLC couldn't have happened without them, and other characters make it clear that they are no less dangerous for their deteriorating sanity.
The player character in The Elder Scrolls III: Morrowind can be this — there is a book called Hanging Gardens of Wasten Coridale. It is written in Aldmeris (an extinct ancestor language to several of the modern languages) and Dwemeris (an extinct language which scholarship does not know how to translate) in parallel. The twist is that if you read the book, as you will when you pick it up, it not only assumes that your character knows Aldmeris but also that you can use it to translate Dwemeris — even if your character is as dumb as a brick and completely focus on combat skills.
Scooter from the Borderlands series is, for the most part, a dumb as bricks redneck stereotype, with limited grasp of social interaction, and a crush on his sister. However, he also happens to be a brilliant mechanic. He's able to build and maintain cars ant teleporters using only the kinds of junk and scrap metal available on the hell-hole that is Pandora. The sequel shows that he comes from the Hodunk clan, who are all stereotypical rednecks with a talent for mechanical engineering.
Arcueid of Tsukihime, even if nobody realizes until Shiki gets involved with her. She has No Social Skills due to her upbringing and Ciel is even astonished that she can actually speak. Apart from her super strength, Marble Phantasm and knowledge of the occult she's a Cloudcuckoolander with no life experience. Actual intelligence is pretty difficult to pin down because of how, well, ditzy she is. If she's not killing vampires, she's somewhere between a hyperactive six-year-old and someone a year or three older than Shiki.
In Hatoful Boyfriend, Cloudcuckoolander Oko San is significantly less mentally developed than the other birds, talks only in 'coo's and is looked upon with disdain as a 'feral' or a 'throwback' to before birds were uplifted. He is also a brilliant athlete and can run faster than he can fly, apparently with enough stamina to beat the human girl in a marathon race.
The player character herself can qualify. She's a Hot-Bloodedcave-dwelling barbarian who couldn't finish the summer reading assignment, and her starting stats show it... but she demonstrates a startling understanding of diplomacy and politics expressed in erudite vocabulary, and if the player makes the correct choices, she can earn the top grades in the class and become a star student, geek out over books in the library, or even become a Teen Superspy. It's explained in the "Bad Boys Love" route that she actually does have a background in politics: her late parents were diplomats negotiating for peace during the fractious aftermath of the human-bird wars.
Largo is a pretty good example. He has, at best, a tenuous hold on reality, but he's a genius when it comes to assembling and programming computers.
Ping also qualifies, being an incredibly complex artificial intelligence system, combat droid and medical diagnosis unit that has been programmed to be a dizzy Satellite Love Interest. The other characters continue to express surprise when she suddenly displays detailed knowledge of her internal make up, no matter how often it happens.
Fighter in 8-Bit Theater often displays a childish stupidity of sorts as well as immense naivety. However he is at times capable of making comments and having thoughts that suggest a higher intellect than one would believe. And as his name suggests, he's a master of armed combat, capable of safely wielding ludicrous numbers of swords at once, including the normally impossible to wield swordchucks. Fighter was a genius for a few comics but then Black Mage stabbed him in the head. He actually managed to store his genius persona in a part of his brain, unfortunately he stored it next to the part that knows everything about swords. The problem being that he really, really, really likes swords.
Similarly, Mega Man in Bob and George is an idiot most of the time, but when he's fighting a Robot Master (or even thinks he is), he comes up with effective winning strategies. This can be explained in that his functions are 1. defeat the robot master and 2. be an idiot, so he always does the second except when he can't since he has to do the first.
Captain Kaff Tagon of Schlock Mercenary is a complete idiot regarding most things, misunderstanding matters social and scientific, and letting his greed get the better of him on numerous occasions. However, when it regards matters of the military or combat, he's at least highly competent, and perhaps a minor genius. The extensive differences between his aptitudes led to this memorable strip. He's also fair at contract negotiations, as far as they concern getting as much money as possible for the job. His idiocy has been toned down, and he is being shown to be more cunning in various matters. For example, he identifies the planet of origin and likely personality traits of one client just from his accent. A bit less impressive given that Tagon was from the planet in question, but still.
Scarlett from Sequential Art is a ditz who has the amazing capability to build Death Rays. She's also easily distracted by watching the washing machine spin round and round and round, and anything shiny. She is part squirrel after all. Turns out she gets less ditzy and more genius when she's near her "sisters" Amber, Jade, and Violet — she used to be a part of "Think Tank" Hive Mind.
Celia. She's come up with plans to unite the Azure City resistance, saved Haley from murderous rogues twice using only words and quick thinking, and even managed to win a complicated legal process while still a student well, it was rigged anyway, but none of the lawyers knew that and the opposition was nervous about her skill, but demonstrates that she lacks some very basic knowledge about humans here. (It's a good thing she didn't try anything exotic with Roy on their date...) Of course, Haley lampshades this.
The Monster in the Dark is obviously as dumb as toast.
Except that here, it instantly sees that she's working with only half a ritual.
Or here, where he not only recognizes Roy, he comes up with a plan to keep Xykon and Redcloak from instantly splatting the Order. Of course, considering where the bad guys head next, it's not a perfect plan.
Several RPG-based comics seem to use a combination of Fighter and Gourry as a template: Hero of RPG World and Karn of Adventurers! come to mind.
The Last Days of Foxhound: Mei Ling is portrayed this way. Otacon is even worse, spending the entirety of the comic thinking the nuclear equipped walking death-mobile he's building is actually a missile defense system. All the while laughing at GIFs of Penguins falling into water, believing everything his Corrupt Corporate Executive boss tells him, trying to rationalize the need for making a stealth missile for his pet project, playing with action figures on the job, and misplacing his instruction manual for the aforementioned Death-Mobile.
Jim from Darths & Droids acts like an idiot most of the time in his portrayal of Qui-Gon. As it turns out, he's taking a Ph.D. in Geophysics, and simply acts stupid because he roleplays in his downtime and "He likes to turn his brain off."
Jo Starr from Cheer! is a Cloudcuckoolander who talks to squirrels. She's also an absolute genius when it comes to analyzing motives and relationships.
The Law of Purple: Lynnah comes off as this at first, though she proves to have a much more developed personality later on. Her genius ability to is be a Bad Ass NormalAction Girl. A more recently-introduced minor character, Kitty, seems to fit the trope much better, though she does get annoyed when her coworkers at NASA don't always take her seriously as a result.
Sam Starfall from Freefall has no knowledge of physics and is the laziest sqid you will ever meet...but is unmatched in the art of thievery and picking locks. Prisons won't take him any more because he stole the cell doors the the last time he was there. He's also a master improviser - Got the Mayor to say "This is a direct order. Hit me with a pie." in the presence of no less than 4 AIs, then on a later scam got one of the said AIs off scot-free by Playing Possum in their arms.
John Egbert. In the beginning he was always goofing off, pulling pranks and acting like a kid, but he used his knowledge of programming and data structure to figure out the alchemization system very quickly, and at this point is easily the strongest of the protagonists... though he came into that status unintentionally and pretty much by accident. Similarly, his sister Jade Harley is a Cloudcuckoolander ... who happens to have a working knowledge of robotics and nuclear technology, is successful at selectively cloning and breeding frogs to create a perfect god-frog in less than 24 hours, and is the one who both formulated and is about to execute the plan to save both the kids and the trolls from their impending doom.
Jade has likely since passed John as strongest character, now being a combination of an entity with deep knowledge of the game world, an omnipotent dog, and and a God with powers over space itself.
Gawaine in Arthur, King of Time and Space seems to be the classic Dumb Warrior in the Fairytale Arc, but in the Space Arc, he's the ship's engineer ... and still often comes across as a Dumb Warrior. According to Fairytale!Arthur "Gawaine's not stupid. He just hasn't any retention for what's outside his field of interest." This is engineering in the Space Arc, the roll of arms in the Fairytale Arc, and computer science in the Contemporary Arc.
Doug from Phil Likes Tacos is a computer genius, to the point that the FBI were after him. If it wern't for his immaturity, he could get a job in tech field.
Clara of The Guild is beginning to show a streak of this. In Season Five, Episode 4, she says in response to Tink's complaining that no one will let them use their booth to sell T shirts, "Well, it really doesn't make sense for these vendors to cut in a middleman, Tink. Their profit margin barely covers their booth rental and travel cost so they'd have to charge 90% of our wholesale to justify a partnership—ah! Shiny!" Lampshaded by Tink's immediate response, "Wait, you sounded smart for a minute."
Keiji Tanaka of Survival of the Fittest is firmly established to be an utter moron within moments of his entry into V3. However, he has an almost unparalleled skill handling a sword (due to years of practice), to the point where he comes close to defeating an axe-wielding opponent with a broken sabre whilst bleeding to death.
The new series version of Sir Schmoopy, in Unforgotten Realms. In particular, he is a strategic (and loophole-finding) genius, who has, for example, figured out a way to survive blowing himself into a billion pieces. On purpose.
Homestar Runner is a bit of a Cloudcuckoolander, refers to the star on his trademark shirt as "a pointy duck" and his supreme honesty makes him somewhat naive, but he is the star (no pun intended) athlete on Coach Z's team. He's also pulled a fast one on Strong Bad at least once, and recited Coulomb's law correctly when asked what 2+2 was. He then said 2+2 was 22.
The Nostalgia Critic can be very silly and not all there, but he's eloquent when not swearing up a storm, is very fond of black-and-white movies and has a brain when it counts.
Motor Ed from Kim Possible is an unparalleled mechanical and engineering genius, so much so that Drakken has to turn to him for help when creating a doomsday vehicle. He's also an extremely ditzy rocker archetype who cares more about his mullet and cruising on some hot wheels than anything else. His plans often involve using his genius skills for some almost moronically simple goal, like stealing a rocket that could easily destroy everything for miles simply to make a hotrod to cruise down the highway with.
Randy Marsh is a brilliant scientist, but otherwise a complete idiot.
Cartman can come up with crazy villainous schemes and speak Spanish and German fluently, yet is otherwise dimwitted and clueless.
Stimpy from The Ren & Stimpy Show is a complete idiot almost entirely lacking in common sense and logic, and often comes across as a drooling retard. However, he spends a great deal of time in the show tinkering around in a laboratory, creating various scientific inventions which work surprisingly well (though, being created by Stimpy, they're usually not very practical, to say the least.) Stimpy has been shown to perform experiments on brains, and performed brain surgery on Ren, successfully replacing Ren's brain with a telephone so he and Ren could play together (something "smart Ren" would never do on his own accord.) For someone whose alter ego is named "Doctor Stupid," Stimpy can be quite the scientist. He's also smart enough to brush his teeth, while Ren usually forgets to.
Hoagie aka Numbuh 2 of Codename: Kids Next Door has a great talent for building and flying planes, but is otherwise a bit of a doofus. In later seasons, he shows more competence, with the Idiot Ball now passed to Numbuh 4. His mother, Betty Gilligan, seems quite ditzy but is capable of using her son's 2x4 technology.
In one episode of Daria, Brittany shows herself to be a tactical genius in a game of paintball. The cheerleading really seems to pay off in this episode. In another episode, when Daria is worried about her self image, it's actually Brittany who knows just the right thing to say.
Invader Zim's titular character is a scientific and engineering genius, repeatedly showing himself capable of building devices beyond even those of his own species, such as a nigh-invincible nanotech exoskeleton, a time machine, a device capable of turning house pets into civilization-destroying abominations, and a monster capable of extracting energy from devouring anything. Zim could probably have destroyed Earth in a day, had he not been utterly incapable of common sense — his inventions always blow up in his own face, usually through no-one else's fault but his own. He's also more than capable of using the gullibility and general idiocy of humans to his own advantage in certain cases.
The members of the band Dethklok in Metalocalypse are completely incompetent at anything not related to music, partying, or contract negotiation. On the latter subject, they can out-negotiate the devil. And even then, while they have those skills, they have none of the skills one would deem necessary to be good at those things. Skwisgaar, who writes the guitar lines and bass lines, and Toki, both of them the best guitarists alive, cannot read sheet music, and both Skwisgaar, Murderface & Toki do not know how to tune a guitar. Nathan, the guy that writes the lyrics, has lots of problem expressing himself, can barely read and seems to have a severely limited vocabulary when talking (but evidently, not when writing songs), in fact, he didn't speak before the age of 5. Lastly, despite their negotiation skills, they have no idea of the value of money or even how to manage it. Really, Dethklok's general level of competency depends entirely on what makes for the funniest scene.
In Disney's Gargoyles, Broadway is initially portrayed as being generally less intelligent, or at least less erudite, than the other gargoyles. For one thing, he started off illiterate; for another, he seems more susceptible to pop culture influences; Hudson had both of these qualities, but he was also a canny veteran warrior. He's also the Plucky Comic ReliefBig Eater. However, he matures rapidly through the series, unleashing the soul of a poet, and becoming a skilled detective as well. And, naturally, a fine chef.
Professor Farnsworth is a babbling old fool most of the time, but he is unmatched in the field of creating doomsday weapons. He never really uses them, though, except to save the Earth.
Farnsworth: I suppose I could part with one and still be feared...
Amy is usually known for being cute, ditzy, and occasionally, somewhat immodest, but she did make a scientific theory on the Earth's rotation and how it works, explaining an invention that can use electricity to polarize it from the Earth's core. It was also part of the plot being that alien cats would take over and transfer Earth's rotation to their dying home planet. She is an engineering student, after all. As the fourth made-for-DVD movie showed, Amy is also an ace player with the mini-golf putter.
Bob falls into this category, as he is generally stupid and naive, but he is excellent at making Krabby Patties, doing math, and art. He was once able to calculate the number of hours left in a week, in his head, in less than five seconds.
Patrick, too. In at least one boating episode, he was shown to be perfectly accurate behind the wheel, as he could give perfect instructions to Spongebob simply via a large telescope, sometimes while barely paying attention, and in another episode, he even GOT a boating license despite not knowing everything there is to know about boats.
Lemongrab is revealed to be a highly competent yet still crazy inventor in "You Made Me!" as he demonstrates surprising knowlege of how to build things that can non-lethally hurt and incapacitate people. His known inventions include an electrical torture chamber, and a "Sound Sword" powered by the frequency of his own screams, which fires sound blasts at people and KO's them. Until this specific area of know-how was revealed, fans just assumed that Lemongrab was borderline retarded and completely inept in all areas of his life.
Finn comes across as this sometimes, too. He's a goofy, somewhat foolish young teenager, but his strategies and imagination are utterly brilliant, and have saved countless lives.
Bulkhead is revealed to be Cybertron's foremost space bridge expert. Professor Sumdac and his fellow Autobots refuse to believe it, assuming that Blurr (and Megatron) got his intel wrong. In addition, Bulkhead is apparently a pretty good artist.
Sumdac himself probably qualifies. He's a master roboticist (even if he cribbed most of his best stuff from reverse-engineering Megatron), but he occasionally forgets to do important things like eat, sleep or make sure there's a legal record of his daughter's existence.
Wallace from Wallace & Gromit is a good example — he's pretty clueless, but he's also an inventor of machines, which, except for regularly going spectacularly awry, seem to work pretty well. In his introductory short, he manages to make a working moon rocket out of items found around the house. The book Cheese Lover's Yearbook introduced a number of non-filmed gadgets of his, such as the Recyc-O-Matic. The fact that when said out loud this includes "Psycho" is significant, because after he put arms and wheels on it, it proceeded to run amok, recycling building fronts and people's clothes before crashing into a brass band.
Chris is good at drawing... or at least used to be. They had an episode about and showed it a few other times, but then they apparently forgot about it. Chris also has a good knowledge about drugs, as shown in the episode where Lois and Peter get high before a talent show.
Peter himself knows a lot about pop culture, KISS in particular. He's also a skilled musician, able to sing and play trombone, and when he's drunk, he's a piano virtuoso with presumably no prior training.
No one beats Lois when it comes to drugs. She computed the street value of uncut Nicaraguan cocaine in her head.
Teen Titans has Beast Boy. Normally the Plucky Comic Relief, he's also very Genre Savvy, and in the penultimate episode, he rallies the four remaining Titans and gets pretty close to taking down the Brotherhood of Evil, before they get caught. But of course, then Cyborg, Starfire and Raven, among others, pop out of the woodwork when it was thought they were frozen like the rest. Beast Boy continues acting as leader until Robin is unfrozen, however.
Danny Phantom has Bumbling Dad Jack Fenton, who doesn't seem very smart, but invented probably half of the Fenton gadgets. He's also a very competent fighter, as a very dismayed Vlad found out. He's also stated to have had solid "B-"s during his school years.
Ruby-Spears' Mega Man has Brain Bot, a genius robot (who wears glasses, natch) who, while being a great mechanic, doesn't seem to have any concept of appropriateness; he tries to "repair" an already-working jet while it's airborne.
Coop, of Megas XLR, is a bumbling idiot who creates half the problems the cast faces, is obsessed with video games (world champ) and eating (also world champ), and lives in his mom's basement. However, he's also a remarkable engineer, able to rebuild a robot from the future, and a skilled pilot, able to pilot said robot, even with its...odder... modifications.
A great deal of the cast of The Simpsons falls into this category.
Homer himself, despite being famous for his bumbling ways, is capable of almost oddly remarkable talents when the episode calls on it, and is consistently shown to have a professional standard ability with the piano. Homer has been seen speaking Japanese, Chinese, Spanish, and penguin. He also seemed to be well on his way to understanding Hindi while eavesdropping on an argument in that language.
Bart is even more noteworthy, as he's sometimes depicted as being not too bright...yet he's been shown to be a remarkably gifted linguist, learning the French language by mere observance and more than couple times acquiring at least competent grasp of an entire language in record time. He can just as quickly unlearn however. Bart also creeps into the Book Dumb category with this quality. Bart also mastered Spanish on short notice for a family trip. That their destination was Brazil made the feat only slightly less impressive. Throughout the series, Bart has also been seen speaking Japanese and Cantonese. He also seems to have at least some proficiency with Latin. Bart may have inherited this from Homer.
Ralph Wiggum. One episode had him playing a very talented George Washington in the school play. Or that he's a good Machiavellian politician, somehow uniting the Democrats and the Republicans in Springfield's presidential election by staying politically independent, and drove some effective campaign to get the majority of Springfield's votes.
"The Boys Of Bummer" revealed that Lenny is an author of mystery novels that are praised by Stephen King.
Sewer Urchin from The Tick is ineffectual, annoying, and smelly, but when The Tick and Arthur need his help to do crimefighting in the sewers, he proves to be the "apotheosis of cool".
Wally from Young Justice. Robin says that they need a dumb, illogical idea to find Red Tornado. Cue everyone turning to Kid Flash:
Kid Flash: As a matter of fact...
Philly Phil from Class of 3000 has, at best, average intelligence. However, he can't be beat when it comes to building devices at the drop of a hat.
Skeeter from Doug is a ditz in day-to-day interaction through and through, and he has a phobia of taking tests. When he ends up taking a standardized placement test without realizing it was a test, he gets a perfect score, and it's revealed that he's actually amazingly skilled in mechanics. This goes unmentioned for the rest of the Nickelodeon run, but it gets brought up now and then in the Disney run.
Played with in various Rocky and Bullwinkle story arcs, as Bullwinkle, generally a dimwit, frequently demonstrates unusual talents for the sake of a specific story. For example, he was called in as an expert on boxtops to crack down on a boxtop counterfeiting ring, his bunion could forecast the weather, he could tame lions with a harmonica rigged from a comb and some tissue-paper, he could remember everything he ever ate in his lifetime (including a secret formula for a silent explosive that happened to have been written on a banana), and possessed a skill for making shiskabobs that bordered on expert swordsmanship!
Wildcat of TaleSpin. Genius at repairs: once fixed a phone smashed with a metal bucket in ten seconds. Knows enough about flying to handle the Sea Duck (although he lacks basic directional skills and can't match some of the more skilled pilots, especially Baloo). Otherwise downright childlike. Word of God claims Baloo and Rebecca were meant to foil each other in this regard. Baloo is extremely Book Dumb and slovenly, but also streetwise and resourceful due to his adventuring (as well as being a grade A Ace Pilot). In contrast Rebecca is well educated and has profound business ethics, but due to her pampered lifestyle is somewhat naive and inept to the outside world. Depending on what the scenario fit, either character would play The Ditz while another would act as The Straight Man.
Professor Moshimo of Robotboy, great at robotics and most other scientific pursuits, proceeds to give a ten-year-old a robot the military would kill for. To make matters worse the robot itself has the intelligence of a child.
Launchpad from DuckTales and Darkwing Duck. Despite being an incredibly incompetent sidekick, he built the Thunderquack (Dark's plane) all by himself and is apparently a brilliant mechanic. He's even better flying the thing! Landing it, on the other hand... Not so much.
Cleveland Jr. from The Cleveland Show generally acts like a childish idiot, however he is skilled with math, science, and rapping.
Luanne Platter from King of the Hill was generally a naive airhead but she was an incredibly gifted mechanic... or least she used to be.
In the early episodes of KaBlam!, June could be this. She was a whiz with technology, and had some inventions of her own....however aside from that, she was dumber than rocks. Please note that this was season one only.
Ed from Ed, Edd n Eddy. A bit of a moron most of the time...but a near encyclopedic knowledge of B-grade horror and sci fi movies, an unusual talent on the flute, some of the odd non-sequiters he says are rather profound and he saves Eddy from his abusive brother not by beating him up, but by pulling the pin holding a hinge together, causing the door to slam on Eddy's brother's head, knocking him out.
Dudley Puppy is a complete idiot... until it comes time for him to fight villains as a secret agent, where he shows surprising cunning and planning ability.
Avatar: The Last Airbender has Sokka, who is often portrayed as the lovable idiot, has a lot of awkward moments, and gets caught in a lot of bad situations. But, he's also shown himself to be highly intelligent. He's the "ideas guy", he's the one who comes up with solutions to the many problems the group runs into. He plans out the invasion of the fire nation, and even helps invent some submarines
Camp Lazlo: In "Prodigous Clamus" it is revealed that Clam - who is either The Ditz or a Cloudcuckoolander depending on the episode - is both an artistic genius (able to create an exact copy of the Mona Lisa in 30 seconds) and a musical genius (able to play an entire symphony by blowing across the top of a bottle).
Johnny Bravo is socially inept and idiotic (with the later being played up more during seaons 2 and 3) but he is fairly competent at martial arts (at least in the first season) and he does have a rather impressive knowledge of things like Beef Jerky.
Pinkie Pie in My Little Pony: Friendship Is Magic is a high grade Cloudcuckoolander, but has a natural talent for throwing parties, a lesser talent in baking, and possesses an absolutely perfect memory for details regarding her friends to the point that she successfully reunited two long lost lovers with a glimpse at the right clues. She's also an incredibly talented musician, and with this skill, was the only one who knew how to save Ponyville from a ravenous swarm of insects. She is also Crazy-Prepared. AND she may have amazing technological skills assuming she made her helicopter-thing (from Gryphon the Brush-Off) and her Party Cannon herself. She seems as wrong-placed in a silent library as her loud party cannon. That doesn't keep her from finding books there much faster than even Twilight (who lives in a library) or Spike (whose main task is in assisting Twilight in the library)
Come to think of it, Twilight herself is a pretty good example; academically brilliant and a pretty powerful spell-caster, but No Social Skills whatsoever and so severely introverted that Princess Celestia had to get her to make some friends as a homework assignment. She's getting better.
T.J. Detweiler from Recess is a genius when it comes to coming up with his latest schemes...but everywhere else, he's a ditz.
Bubbles from The Powerpuff Girls is a complete Ditz but is able to communicate with most small animals, is just as good in battle as her sisters and in one episode where Buttercup and Blossom can't get rid of the Monster of the Week, it's Bubbles who figures out what to do. She asks it politely to leave. And it does.
Sterling Archer is a boorish, egotistical jackass who is exceptionally bad at the "tradecraft" parts of spying... but not only is he remarkably good at the "action hero" parts, but he keeps dropping references to people like Alan Turing, Indira Gandhi, and Eugene V. Debs. Wordof God is that Archer treated his school work the same way he treats spying; he'd be competent if he cared.
Pam is terrible at her office job... and is an experienced underground bare-knuckle boxer and street-racer. Similarly, Cyril should not be in the field, but he's a fairly talented accountant and lawyer.
Klunk is just as inept as the other Vulture Squadron pilots, but he's the go-to guy for inventions on how to stop Yankee Doodle Pigeon.
High functioning autistic savants such as Daniel Tammet, while significantly lacking in social skills and maturity, are geniuses. Daniel managed to learn stilted but comprehensible Icelandic in under a week.
Note this may not be because of increased intelligence per se, but because their condition makes them focus on one narrow area of interest to the exclusion of other things.
Lawrence Kim Peek has an unnamed developmental disability due to brain damage. He can answer virtually any question pertaining to historical dates, statistics or any obscure trivia.
Hikari Oe, son of the novelist Kenzaburo Oe, is developmentally disabled and autistic, and the inspiration behind his father's prizewinning novel A Personal Matter. He is also a very talented musician who expresses himself through music, imitating bird calls.
Kanye West is a talented producer and musician in the studio. Outside of the studio, he is so lacking in common sense and basic social graces one gets the impression that he's not all there and-
In the antiques trade, someone who instinctively recognises a genuine antique without any training is a "divvy", probably short for "diviner". Divvies are stereotyped as not very bright (because they often don't actually know anything about antiques, beyond "Yes, that's valuable"), which had led to the term entering general British slang for a stupid person, with or without Genius Ditz qualities.
Truth in television as many people do find that while they are incredibly sharp in one aspect of their lives they may be incredibly incompetent in the other. Like the Maths genius who cannot make people listen to him or the eloquent actor who has failing grades. This is especially common amongst college students, many of whom will say they picked their major at least partly because they're terrible at the perceived opposite (English majors saying they became English majors because they're terrible at math seems to be especially common.)
"A specialist knows more and more about less and less until he knows everything about nothing; a generalist knows less and less about more and more until he knows nothing about everything."
Britney Spears during her glory years. Offstage and during interviews she seems a bit flaky, but when she gets onstage she's a great dancer and performer (or used to be) and one of the most successful pop stars ever.
Likewise with Lindsay Lohan, while sometimes her behavior has people wondering just what goes on in her head, she is nonetheless a skilled actress/singer and can also be very profound and intelligent, like when she did a documentary on child labor in India.
Flavor Flav, while known more for his buffoonish antics including a reality show and wearing a clock around his neck, is actually a musical prodigy. Among the many instruments he can play (and play well) are piano, guitar, bass, saxophone, clarinet, and drums.