This is a specific kind of artistic license, where a pivotal clue in solving a mystery or puzzle is actually erroneous. This is related to Conviction by Contradiction, where a single thing wrong with an alibi is sufficient to prove guilt, but goes further: the key that makes the claim or alibi wrong is itself factually incorrect.
For example, a guy's alibi is that he was caring for his pregnant mule, and he is immediately revealed to be lying, since mules can't get pregnant. We've got him! To the jail! Not so fast: while they're rare, fertile female mules do exist; a mule's foal is precisely what the picture to the right depicts. Thus, there's a problem with this "revelation": it's simply wrong.
When adding examples, keep in mind that a fact has to be actually wrong to qualify for Conviction by Counterfactual Clue. If there's simply a way to explain away the objection without calling factual rightness into question, it's Conviction by Contradiction. Many examples, especially ones with complex contexts, have some aspects fall into one, and others into the other.
This can be sometimes excused by Science Marches On. In many cases, the "clue" started out as Conviction by Contradiction, then science marched it right over here. When this happens, but the ultimate conclusion is demonstrated to be correct, it overlaps with Right For The Wrong Reasons, especially when other clues in the story are skipped over, but are both factual and more useful.
Oh, for the record, it's male mules that are*
A common one seen in multiple detective series is the unwavering belief that all women are physically weaker than all men, which is commonly brought up as a foolproof alibi. Even when there's an elderly, overweight or disabled man in the room who doesn't get the same courtesy. Especially headache-inducing in the Moonlight Sonata case of Detective Conan, where a female nurse is written off as a suspect because she's petite with thin arms and couldn't have lifted the bodies. (Each of which are taller than her and would require quite a feat to move around the way they did.) Then when it's found out "she" is actually a crossdressing man this alibi immediately vanishes, even though he's still the exact same muscleless Bishounen waif.
What makes the argument doubly galling is that Conan constantly travels with Ran, who is an Action Girl who regularly punches chips of concrete off of building corners, puts sizable dents into metal poles, and kicks in doors. No one has any doubts that she is extremely strong. Yet Conan continues to use the argument that a woman is too weak to do certain tasks, in the presence of Ran.
The "mule" clue was used in "The Case of Molly's Mule."
A Two Minute Mystery had a deaf witness's testimony that he read the suspect's lips and took special note of it because the suspect was whispering called into question, because supposedly, he shouldn't have been able to tell the suspect was whispering. However, whispering is just when instead of using your vocal cords normally, you create turbulence with them, producing a hissing sound. This then requires you to use your lips and mouth to create sounds that your vocal cords normally would, and is very noticeable to a lip reader. You can easily demonstrate this by saying the same word as a whisper and in normal voice, and feel how different your mouth moves. Then try freezing your jaw and lips in place and speaking, something you can do mostly understandably with operating your vocal cords normally, but you can't produce meaningful sounds at all if you try it while whispering.
In one Two Minute Mysteries story, a man relates how he leaned over his train bunk and read a headline on the newspaper the man below him was apparently reading. His companion deduced that the man with the newspaper was the perpetrator, because the only way the first man could have read the headline is if the newspaper was held upside-down (and therefore upside-up, relatively speaking, to the first man's eyes.) However, many people can read upside-down text just fine, especially if the text is in a large font and the message short - for example, the text of a headline, or the reader is even mildly dyslexic.
Even without any skill at it, everyone who can read can decipher upside-down print letter by letter. It may take a few minutes, but what's time to someone sitting bored in a train?
Or even easier, if the top half of the paper is folded back while the man reads the bottom.
In "Murder At The Zoo", Haledjian meets with a zookeeper after a doorman working at the zoo is found killed. The zookeeper claims to have been alerted to the murder when he heard the scream of a giraffe, since one of them had been caught in the crossfire. Instantly Haledjian declares him to be the real murderer, because according to him, giraffes have no vocal cords.
The page quote comes from a mystery where one kid with a cast on his left arm is accused of stealing some keys, and in fact they're found in his pants pocket in his locker. However, the "proof" that he didn't do it is found in that the keys are in his left pocket, and, according to Encyclopedia, it's impossible to put keys in the opposite pocket of the hand they're in while running, as Bugs Meany claims happened. It might be more difficult for some than others, and there would be very little logical reason to do so, but it's certainly not impossible for everyone.
In one case, the culprit's alibi was that, when he walked past the victim's house, he heard the electric clock (which was unplugged when the crime was committed) ticking, the contradiction being that electric clocks don't tick. When this was first written, (back in the 1970s), this was Conviction by Contradiction, though questions like "how loud would it have to be ticking to be audible outside the house?" and "exactly how is this an alibi anyway?" might arise. Today, we can skip straight to the fact that some electric clocks — particularly analog clocks in which the second hand jumps from one mark to another and an early kind of digital clock where numbers were written on flaps that showed in succession (as shown in Groundhog Day among others) — do make sounds that, while distinct from pendulum-regulated clocks, are described as "ticking". Additionally, some digital clocks that indicate seconds will play an artificial ticking sound.
One involving a sword from The American Civil War. The guy hawking it claimed it was authentic due to the engraving showing that it was given to Stonewall Jackson by Robert E. Lee after the First Battle of Bull Run. The 'correct' answer was that the sword was fake, because nobody would have called it FIRST Bull Run until there had been a Second Bull Run. Given how long it can take to commission, make, retrieve, and engrave a sword, it's entirely possible that the second battle a year later either already happened or was soon coming, necessitating the need for specificity.
Improved slightly in a reprint of the story by pointing out the much more useful fact that the Confederates always referred to the battle as the Battle Of Manassas, not Bull Run. The reprint also changes the inscription from "Presented by General Robert E. Lee" to "Presented by his men", since Robert E. Lee was neither Commander of the Confederate army, nor anywhere near Manassas at the time — he was in western Virginia, and wouldn't assume command for over a year after the battle. (Had Jackson been awarded a sword after the battle, it would most likely have been Joseph E. Johnston doing the presenting.)
Encyclopedia Brown pinned a crime on a magician because he was wearing short sleeves. He claimed that all magicians wore long sleeves so that they could pull objects out of them, when many good magicians don't need anything of the sort. Many, in fact, wear short sleeves solely to impress people with the undeniable fact they have nothing up them, and at least one performs magic in the nude. There are entire styles of magic that depend on (for example) marked cards, psychological tricks, or props with trap doors, for which sleeves are completely useless.
Worse still: pick up a magic trick guide book, any one. You will not find a single trick that relies on the magician using sleeves.
One case was "solved" (by Sally, not Encyclopedia) because a couple sat in a restaurant with the man's back to the wall rather than the woman's, from which Sally deduced that each was actually a member of the other gender in disguise. This is because of a rule of etiquette that the woman should sit against the wall, so she can see and be seen. For this to be evidence, it would have to be the case that people followed this "rule" with no, or at best very few exceptions; but even putting aside the fact that people from some places don't observe it at all, even in areas where it's well-known it's violated all the time.
Worse: either the couple knew about the rule, but then for what reason should they sit according to their real gender instead of their disguise, or the couple did not know the rule, in which case their sitting order was totally random. Either way, nothing can be deduced, except that a couple sitting in the "wrong" configuration is more likely to not know the rule.
The point which Sobol may have been trying to make was that a) at one time this rule was in fact very well known and followed (keeping in mind the time period the stories were written in—Values Dissonance may apply, since people not knowing or caring about such a "rule" today doesn't mean they didn't in the 60's or 70's) and b) if it was in fact well known, the couple in question, despite being in disguise, assumed the 'proper' seating order out of habit. On the other hand, there may not be proof this ever was a well-known rule, or one always followed, even at the time the books were written; Sobol may have had Small Reference Pools and believed everyone knew of and followed this rule because he/his generation had been taught it. And habits aside, it does seem rather strange that someone planning a robbery would bother to remain true to rules of etiquette...
Another point on this is that the rule is fuzzy anyway, as another form exists: supposedly men instinctively prefer to sit in unfamiliar locations in such a way that they have a good line of sight over any angles of approach, as a fight-or-flight mechanism.
Also, the crime was that the proprietor's daughter was robbed and knocked unconscious in the women's room. Leading up to this conclusion was the assertion that a woman couldn't have overpowered her because of her strength, and a man would have been noticed. There couldn't have been another woman in existence as strong as the victim? After all, the canonical reason the bullies Encyclopedia outsmarts always try to get revenge by outsmarting him back is because of his partnership with Sally, as she's stronger than any boy in their age bracket. The third chapters in nearly all the books explain this, and even call her Encyclopedia's bodyguard.
Another solution was based entirely on the supposed 'fact' that roosters only crow when they saw light (the crime was a con man trying to convince kids he found a way to make roosters crow on command, but actually uncovering the cage so they saw light and thought it was sunrise; he claimed that he would soon improve the device to make hens cluck on command, and that whenever hens clucked, they laid an egg. Now, anybody who has been around a rooster for an extended period of time will know full well that they crow whenever the heck they want, whether the sun is out or not. And, of course, the hen part of his story should have been clearly false, especially since he was targeting the con towards chicken farmers.
One solution in Encyclopedia Brown Takes the Cake relied on the fact that the culprit had used glycerin tears that fell from the outside corners of her eyes instead of the inside, thus revealing them to be fake, as "If only one tear falls, it will run from the inside corner of the eye, by the nose, and not from the outside corner." Only, none of that is true.
In a Mike Mist Minute Mystery by Max Allan Collins in the early 1980s, the title character supposedly identifies a crook because she claimed that she cashed a check using an automatic teller machine, which Mike claims is impossible. Here, the readers wrote in to note that it's done all the time; you enter the correct amount of the value of the check into the machine as a deposit and you are free to withdraw from that amount. And of course, Technology Marches On: you can now deposit a check into (some) ATMs, and the machine is sophisticated enough to scan it and correctly parse the writing as a check amount.
One entry in The Armchair Detective series stated that one true way of knowing if a pre-World War II telegram is false is if the phrase "World War One" or "The First World War" is ever mentioned, on the assumption that nobody could have foreseen a second World War before it started. However, it was used by some almost immediately after hostilities began. Note that the series in general isn't particularly prone to this. In his defense, those were not common terms, and would hardly be included in a telegram where they could easily say "The War" or "The Great War" with fewer letters. It may not be rock-solid evidence, but it's a good reason to be very skeptical.
It should be noted that using them as the actual name of the War would be even more suspicious - although the First World War was, indeed, used, it at first was more of a descriptive term (IE, describing the War as the first World War in contrast to previous, non-global, wars, and, as in the case of the first recorded use of the term, the early-war term 'The European War').
This is Science Marches On, but one of Isaac Asimov's space mysteries hinged on the fact that one side of Mercury always faces away from the sun, because at the time it was reckoned this was true. Later research proved this wasn't the case, which Asimov acknowledged once he learned it — unfortunately, he couldn't see any way to amend this clinching evidence without completely re-writing the story.
In the MonkTie-In NovelMr. Monk in Outer Space, one of Monk's deductions that makes him conclude that a person was killed in a different hotel room and moved downstairs to a different room in a maid's cart hinges on the fact that insulin must be refrigerated. Except it doesn't; diabetics commonly keep vials of insulin currently in use at room temperature, usually due to the discomfort of injecting cold insulin. He also incorrectly states that all diabetics take insulin, when some Type 2 diabetics can control their diabetes through diet and exercise alone, and most can control it with the help of oral medication.
Refrigerating insulin mostly has to do with preserving it longer. Doctors recommend keeping insulin at room temperature for a month at most, while keeping it cold extends this to six months.
One of the subcases in Mr. Monk and the Dirty Cop that is mentioned in a few paragraphs takes the Encyclopedia Brown example used as the page quote. What is known about said case is that it is a man who tripped over a crack in a parking lot and broke his arm, which is locked at a 90 degree angle according to his doctors, yet it is possible to see his car keys in his right pocket, which should be inaccessible to that hand. For all we know, this person could just easily grab their car keys with their left hand — but it is at least good reason to look closer and see if the man's arm were truly injured.
One Encyclopedia Brown-esque story concluded that the suspect was obviously lying because he claimed he was at a laundromat putting clothes into a top-loading dryer. The detective claimed that all dryers are front-loading. This is incorrect; top-loading models existed on the market even in the time period when the story was written.
This happened with Encyclopedia Brown himself. Bugs Meany lied by copying another kid's true version of events, changing washer to dryer but otherwise using the exact same words. The first kid said he'd put the clothes in from the top, and Bugs copied that detail.
The vital clue that solves the mystery in the novel Fatal Equilibrium doesn't work at all once the Fridge Logic sets in. Canoes would necessarily have a smaller price variance only if one assumes all canoes are the same, which is a bad assumption to make when applied to non-theoretical situations. This is even worse when the protagonist makes the comparison of a hammer and a car. Anyone with half a brain would realize that, while the price variance of a specific make and model of car would likely be smaller than that of a hammer, cars in general have a considerably larger variance due to differences in performance, fuel efficiency, mileage, current fads, etc. This effect could actually be even more pronounced in the society under question, which did not have mass production, meaning each canoe would be unique.
In the battle between Archmage Gromph and Dyrr the lich in the War of the Spider Queen series, Gromph realizes Dyrr's shapeshift spell means he's not undead anymore, so negative energy spells can and do work on him. The kicker? He'd polymorphed into a construct, which is still immune to negative energy and a Lich, unlike most undead, CAN polymorph himself as an explicit part of the runes.
In one of the Avatar Trilogy novels, a ghostly figure appears in front of Cyric's mercenary band and threatens them. Cyric, observing that none of the witnesses has aged as a result, concludes that the figure isn't a genuine ghost (which had an aging aura under then-current D&D rules), but a harmless product of wild magic. Not only is there no clear reason for him to assume a product of wild magic would necessarily be harmless, but there are several dozen other ghost-like creatures in the Forgotten Realms Verse that it could have been, that would not age witnesses yet would be extremely dangerous in other ways.
Woody Allen parodied this in a story called "Match Wits with Inspector Ford", where Inspector Ford deduces that a man didn't kill himself, because there was cash in his pocket, and someone who is about to commit suicide would use a credit card.
In real life, indications that the victim who committed 'suicide' was planning ahead for the immediate future (for example, if they made a dinner reservation for tomorrow, then killed themselves ten minutes later) do indeed make police a bit dubious about that suicide, although it's not 'proof' of anything. However, what method of payment they use is hardly relevant to that.
There was this one story where someone said they saw a thief in their house because they held a spoon up and could see the reflection. This was outed as spoons show reflections upside down. I mean, obviously you can't tell it's a person from an upside-down image. That'd just be silly. There's also the tiny detail that reflections are right-side up on the back side of the spoon! Also, let's not forget that there are people who actually can identify a person from an upside-down distorted image, like many serious dyslexics.
In Murder on the Links, the second Hercule Poirot case in terms of internal chronology (though probably not of publication order), Poirot sees a stage act consisting of twin sisters (one blonde, one brunette) and deduces that one of them must be wearing a wig. Because of course it's impossible that twin sisters could be fraternal, or that their parents could be a blond and a heterozygotic brunette (or two heterozygotic brunettes).
In the 1980s and 1990s, the Swedish edition of The Phantom had a page of reader-submitted material, of which one of the more popular were crime mysteries (see Conviction by Contradiction for more details). One of these had the culprit give himself away by referring to the banana as a fruit. Even though banana trees are herbaceous plants, a banana is biologically considered a fruit. Even when using the culinary term for fruits (which is probably the term most people outside of the fields of biology, botany, and horticulture are familiar with), this still doesn't exactly excuse the conviction, as the banana is one of the most classic examples of a "Culinary Fruit." (For a more specific description, a culinary fruit is any edible fruit that is sweet. Biologically, a fruit is a plant structure that contains seeds. This is why things like tomatoes, peppers, eggplant, and cucumbers are classified as fruits by botanists, but not by chefs.)
The trope is invoked and lampshaded in Welcome to Tranquility. Emoticon is in jail and being questioned with regards to the murder of Mr. Articulate, a crime-solving member of the community who was legendary for his intellect, wit and long and storied history of traveling the world. However, Emoticon points out that a lot of the stories of his adventures were "culturally insensitive", and he recounts one of the detective stories from Mr. Articulate's youth that always stuck in his mind: Mr. Articulate discovered the identity of the murderer because the "Korean" man at dinner left his chopsticks in his bowl of rice, something no actual Korean would do since it is a symbol for death and, therefore, he must not be Korean, but Japanese instead, and thusly the killer. However, Japanese culture has the same custom. "So the ending doesn't work. It's a cheat."
Of course, Koreans eat rice with a spoon, so there's one more reason it doesn't work. They eat other dishes with chopsticks.
Also parodied, along with The Famous Five and The Daily Mail, in the Viz comic "Jack Black", where a 1940s boy detective with somewhat conservative views would use the most spurious of inconsistencies or counter-factual clues in a person's story to reveal them to be the week's villain (perpetrators of such dastardly deeds as using fake wooden pips to fool people into thinking that "cheap" raspberry jam was "luxury" strawberry jam). Often the villain would be sentenced to death or a comically excessive prison sentence for their "crimes".
In the 1944 Sherlock Holmes movie The Spider Woman, Holmes deduces that a series of apparent suicides were really murders because "suicides invariably leave notes behind them," and none of these people did. Actually, no more than about 20% of suicides leave a note.
In the movie Soultaker, a cop investigating a fatal car crash finds it odd that the doors of the car are both wide open. He doesn't buy that a closed, even locked car door could fly open if the car were to crash, and asks his partner, "What are the odds?" In reality, the odds of both doors of a two-door car being flung open in a high speed head-on collision are pretty goddamn good. This didn't escape notice when the movie was featured on Mystery Science Theater 3000.
Live Action TV
A rather amusing in-universe example in Star Trek: Deep Space Nine. When O'Brien is marked for death by some crazy aliens because he's one of the last people alive who knows how a forbidden superweapon works, they send a bogus video back to the Federation that shows him dying in an accident. His wife realizes something's fishy because he's drinking coffee in the video and she knows he never drinks coffee in the afternoon, when the video was supposedly taken. But then after the plot is foiled and Miles comes back home, as he's settling in he asks for a cup of coffee. She reacts with astonishment, and he says he drinks coffee in the afternoon all the time!
In an episode of Judge Judy, a man is trying to collect money owed to him by a woman who rented a room from him. He says he provided her with an invoice each month and brought copies showing how much the woman owed him. The invoices had the invoice date on each of them, but they also had a date in the header or footer showing the date they were printed. Judge Judy points out that these invoices are fake because they all have the same date. The guy made the argument that the invoices were created when he said they were, pointing to the invoice dates, but the other date was the current date, the date he printed them. Judy said something like, "I'm not stupid, you know," and ruled in favor of the woman who owed him the money, because apparently to her it's impossible that anyone printing a copy of something would record the date the copy was printed.
Actually, Judy might have a point there - Invoice copies are supposed to be printed on the same date as the actual invoice. Had this been in a real court of law and not Judge Judy, people would actually be getting suspicious, and a real lawyer would probably dismiss this as evidence because there isn't proof that the invoices weren't tampered with.
Would you believe CSI: Crime Scene Investigation is accused of this? In perhaps the most memorable chain of cases ever, the identity of the Miniature Killer is revealed by bleach, the only linking thing in the four mini-crime scenes. However, one of them was listed not under the name 'bleach', but by its chemical name, NaCl. NaCl is sodium chloride (table salt) while bleach is sodium hypochlorite (NaClO).
Lampshaded in another episode. Captain Brass decides to reopen an "accidental death" case after he sees the supposedly bereaved husband coming out of a club to hop into a brand new sports car. He later tells the husband that his (Brass') suspicions should've been aroused earlier - when he interviewed the husband, the man said that he "loveD" his wife, and Brass' experience was that innocent people never referred to their loved ones in the past tense so soon after their death. *
Although he also notes that this is not always true, even in his experience, but it's been true often enough that he should've realized something was wrong at the time (presumably, some cases of past tense involve couples who fell out of love or were having marital problems).
While this obviously (as the accused's lawyer specifically points out) means little legally, it did give Brass more reason to pursue his new suspicions.
And there's an episode where Catherine suspects a mother assisted in a murder her son took part in because a body bag found at the crime scene was neatly folded, and Catherine said, "Teenagers never fold things, mothers do!" Apparently clean freak teenagers do not exist in Catherine's mind.
In another episode Catherine (again) catches a woman who killed her daughter by which way the woman was looking when she was talking to Catherine. Catherine deduces that the woman was looking left and therefore lying, the woman did confess after being caught, but their whole case would be hinging on this, when people who are experts on lie detection and reading microexpressions say that statistically people are more likely to look straight ahead when they are lying.
In the Leverage episode "The Homecoming Job," Sophie realizes that a Sleazy Politician lied to her about something because he looked her right in the eye when he said it. According to her, the only time any man ever looks a woman in the eye is when he's making a special effort to lie to her.
A bit better than other examples on this list, because this one was more a snarky line than a serious deduction.
It may have been snark, but it was also based on truth. Some of the latest research indicates that people who are lying are more likely to look you in the eyes to make you believe what they're saying and people who are comfortable in what they are saying tend to look in any direction they feel like because they don't need to fully concentrate on what they're saying.