Portgas D. Ace of One Piece has only ever received a handful of scenes (not counting a short period of anime Filler), none of which delved very far into his character. However, some fans still came to imprint a completely straight image of The Ace on him, to the point that when he actually got a little backstory and turned out to be more of a Broken Ace, they complained about the whole affair.
Team Rocket from Pokémon occasionally manages to remind both the cast and the audience that they can be a competent threat. Two notable episodes are the Johto episode "The Stolen Stones", and the Hoenn episode "Do I Hear a Raltz?". Both of which features the heroes fighting off TR throughout the bulk of the episode, instead of the usual five-minute Curb-Stomp Battle. The newest incarnation of the series has taken this concept and run full steam with it.
In the Pet Shop of Horrors manga, Tetsu goes from a being a cunning murderer to being a cute, child-like comic relief after his first appearance. In one of the final volumes, however, he briefly shows as a bloodthirsty demon again, when the situation calls for it.
Lupin III doesn't carry a sword and almost never has call to use one, preferring to let Goemon handle the cutting of useless objects. However, in the manga, he and Goemon met when Goemon was ordered to keep him from stealing the Zantetsu-ken formula, and it's noted that Lupin's stolen plenty of forging scrolls and kenjutsu teaching scrolls over the years. This backstory isn't consistent with the anime (though each character's backstory seems to change to suit the episode/movie in question), but on those rare occasions where he's handled swords, he's been shown to be quite competent with them, and when handed the Zantetsu-ken he's pulled off some jaw-droppingly accurate and fast cuts, on par with the stuff we normally see Goemon do.
Kyouko is Flanderized into a complete ditz with a pathetic schoolgirl crush on Sasaki for most of You Got HaruhiRolled!. She is still like this in Chapter 84, but bits of her canonical personality — that of a cheerful Anti-Villain who is actually competent — shine through in her discussion with Fujiwara.
Ned Flanders himself had this happen in The Simpsons Movie, as Bart becomes annoyed with Homer's Jerk Ass ways, and begins viewing Flanders as a better father figure who's very caring, if still quirky. This was a return to his extreme-Nice Guy roots, while the show by this point had turned him into a Strawman PoliticalFundamentalist.
The Star Trek: Deep Space Nine novel The 34th Rule (no, not thatRule 34, the 34th Rule of Acquisitionnote Which is "War is good for business"...), features Ferengi Grand Nagus Zek thinking up a highly intelligent and deadly serious scheme to gain profit — and it succeeds magnificently. The Ferengi were always supposed to be supreme businessmen and expert swindlers, but on TV they quickly morphed into comic relief after failing to work as a threat on Star Trek: The Next Generation. The comedy overshadowed the other traits so much it got to the point where the supposedly master schemers could be easily beaten at their own game by having an attractive woman flash her eyes at them. In this novel, though, Zek reaffirms the initial Ferengi reputation for ingenious profit-making. Word of God confirms that this was part of the novel's purpose: reverse the Flanderization of the Ferengi.
In macrocosm, the Star Trek Novel Verse generally tends towards reversing the Ferengi Flanderization whenever possible, and while Ferengi are still portrayed somewhat comically at times, many times we get to see Ferengi be competent in battle, be damned persistent villains, and we even get to see good guy Ferengi use their capitalist natures to pull off some impressive plans.
In his very first appearance, the short story "Neutron Star", Beowulf Schaeffer of Larry Niven's Known Space series was explicitly described as being "limber enough to smoke with his feet" (that is, holding a cigarette between his toes and using his feet as hands). While subsequent stories always had him be agile and quick, this level of flexibility never resurfaced again until "Borderland of Sol" (written nearly ten years later). When a bad guy ties Schaeffer and his partner to a support pole, Schaeffer kicks his shoes off and proceeds to free the two of them, using his feet as hands. It's even explicitly mentioned that the villain, being a thickly built Jinxian, would never think that a person could be that limber.
In E.W. Hildick's The McGurk Mysteries series, in the first book Mari Yoshimura appears in, she martial arts kicks a man unconscious. This was handled fairly realistically note Mari kicked him in the back of the head when he was completely unsuspecting, and insisted that she'd have had no chance in an actual fight. Her martial arts ability wasn't even mentioned again until 4 books later in the series, when she was able to use an armlock to subdue a boy her own size, and never again after that.
Invoked by Gaius Sextus in Captain's Fury, fourth book of the Codex Alera. He says that part of the reason for the realm's internal strife and ongoing civil war is that the High Lords see him only as a weak, scheming old man, so he sets out to remind them just what he's capable of when you push him.
He's also a professional warrior/trainer. In spite of his reserved British character and his understandable tendency to leave the physical monster bashing to his superhuman charge, he is quite capable of beating the tar out of an old associate, menacing his supposed employer and thrusting an epee through a senior official's chest. Not for nothing, after all, was he once nicknamed "Ripper."
After being shot in the ass by a crossbow, he managed to pull the bolt out and use it to stake a demon in one motion.
In Monk, Lt. Disher was flanderized from Plucky Comic Relief to a borderline The Ditz. Thus, it fit this trope later on when he would demonstrate competent policework. He's actually so good as an officer that the season finale has him become a police chief in a New Jersey town.
In Boy Meets World, Eric Matthews was flanderized from the cool, rational older brother into an irrational Cloudcuckoolander except for one of the series' very last episodes, in which he was suddenly portrayed with something resembling his original characterization (which was lampshaded by the others who point out that he seems especially well rested).
The Cat from Red Dwarf is portrayed in the first two series as knowing the ship quite well, and his senses are heightened compared to the other characters. However this doesn't come across as important to the viewer as his character is mostly self-centered, anti-social and completely obsessed with eating and clothes at this point. We generally consider him to be completely useless due to his unwillingness to be friends with the other characters. Later his skills come in handy - he pilots Starbug due to his knowledge of ship controls, he has excellent navigation and prediction abilities, is able to detect danger, and in general his dialogue indicates he knows the characters better.
In later seasons, the Cat is occasionally even shown to be able to detect or track objects in space by pure sense of smell.
Whenever the crew get into fights, expect Cat to demonstrate an unerring ability to dodge or catch anything thrown at him. Even the rest of the crew tend to forget that he's, well... a Cat?!
In the second season Star Trek: Deep Space Nine episode which introduces the Jem'Hadar, Quark shoots dead a Jem'Hadar soldier who was about to kill Sisko without much thought or effort. When Quark kills Jem'Hadar in similar circumstances in Seasons 6 and 7, it is written and played as if it's a momentous moment.
Speaking of Jem'Hadar, they rarely used their clearly advantageous invisibility. In "Blaze of Glory", while Sisko and Eddington are in an area attacked by the Jem'Hadar, Sisko shoots a cloaked one, while Eddington is glad one of them remembered they could do that.
In the show The Office, Steve Carrell's character was promoted to manager because of his amazing sales skills yet the audience often sees him as a buffoon based on his actions and interactions with others. Many episodes in later seasons have him going back to sales to remind the audience that he is actually competent.
In the fourth series of Merlin the titular character is about to be killed by the Monster of the Week, only to be rescued by a sword-wielding Guinevere. Arthur is surprised and delighted at her bravery, even though she displayed similar skills with a sword way back in series one.
The Adventures of Brisco County, Jr.. Brisco is a graduate of Harvard Law School. This fact was actually forgotten by everyone in all the cowboyesque action-adventure. And then came the late season episode in which he needed to be a lawyer and not a gunman.
An episode of Tru Calling had Tru, pretending to be a nurse, asked a question by a real staff member that required extensive medical knowledge. Which would have been a problem if Tru wasn't a med student. The show did try its best to make you think she'd been caught, so they must have figured at least a fair few people would forget.
Anthony Kiedis of Red Hot Chili Peppers was once known as as a guy who rapped in an over the top funk voice, before changing to singing. This led many to think he'd lost his sense of fun. However, on the songs "Tell Me Baby" and "Storm In A Teacup" he resurrects the old voice.
Used for humor in Yu-Gi-Oh! The Abridged Series a few times. For instance, Tristan has been so completely recast as the The Ditz that the sight of him showing up on a motorcycle seems out of character... despite being completely in character for him in the actual show.
Directly invoked in an episode where Tea plays a card game against a penguin, much to Yugi's shock... and Yami's lack of shock, since she's been playing card games since the beginning of the series. And often winning.
Squidward from Sponge Bob Square Pants does occasionally get the chance to display some actual musical or other talent. He was, in fact, initially characterized by Plankton as a "mediocre clarinet player," but has usually been shown as an abysmal one.
Though if you watch a lot of the show, he seems to have a good grasp of music theory and of culture and seems to be able to read music well. He might be having issues playing a clarinet due to having no fingers.
Additional talents for other characters are underplayed or diluted due to Flanderization, but still appear every now and then. Spongebob, for example became increasingly idiotic and tends to cause more problems in his workplace than good, though some episodes still point out he is a highly competent fry cook.
The Simpsons: It's revealed in "A Streetcar Named Marge" that the Trope Namer is muscular, which isn't seen often. It's seen again at the beginning of the episode where he moves to Humbleton. When he moves back, people probably forgot again and then he showed his strength by defending himself against another muscular man. Because of the gratuitousness of Ned's topless self, this shades into Brick Joke as well; the writers probably just thought it was funny.