Played straight for most of the 2006 remake of The Pink Panther... mostly. As an example, after hearing a murder victim's last words were "Oh, it's you!", Clouseau orders all people in the city with the name "Yu" to be detained for interrogation. Naturally, he's saddled up with a Chinese woman rattling off in Chinese. After the interrogation, his partner asks if he can even understand Chinese. Clouseau acts all offended and replies something along the lines of "Do you think I would do all this if I didn't understand Chinese?". Seeing as he's been Feigning Intelligence for most of the movie, his partner (and the audience) look unconvinced... until the end of the movie when a flashback reveals not only was Clouseau telling the truth but the woman gave him a vital clue.
In the original film series, Peter Sellersoften commented that he played Clouseau as an extremely arrogant man who was nevertheless just clever enough to realize what a complete imbecile he really was.
Otto in A Fish Called Wanda, who liberally quotes Nietzsche. Wanda manages to see through his pretensions by the midpoint of the movie.
Done as part of a Gambit Roulette in the 2007 St. Trinian's. It helps that they know some of the answers.
An unintentional example in the second Tremors movie, when the Graboids first mutate into Shriekers. For the first few scenes after they come into existence, they tear up several cars and the radio tower, convincing the protagonists that they had achieved human-level intelligence and had actually planned everything out to cut off their ability to travel and communicate with each other. Eventually, they find out that the Shriekers navigate by infrared, and were simply biting anything they came across that was hot, whether it was actually food or not.
Grady: You mean they're acting so smart because they're so stupid?
Dodgeball has Ben Stiller's character attempt to impress a woman... by pretending to read the dictionary.
Owl in Winnie the Pooh. When faced with a note that contains more than three words, none of which are his own name or "Thursday", he first tries to trick Rabbit into reading it for him, and then considers pushing Rabbit out of his tree rather than admit he's having problems.
Rabbit is another example of this trope, to a lesser extent.
Discworld's Fred Colon sometimes does this when talking with Nobby Nobbs. Nobby Nobbs has an unfortunate habit of asking questions (it's implied he's the smarter of the two, but not by much)
The Number of the Beast by Robert A. Heinlein features a main character who not only passed himself off as an expert, but managed to get a degree by writing a paper that catered to all of the reviewers' prejudices and pet theories. Of course, he was actually doing this to prove a point instead of trying to fit in with educated society.
The main character in The Death of the Vazir Mukhtar is sometimes accused of writing or at least editing the correspondence of General Ivan Paskevich, his in-law and sort-of superior in the Caucasus, so as to make him seem smarter. That is apparently untrue, although Paskevich might be considered a mild example of this trope nonetheless.
As did Lisa Turtle in an episode of Saved by the Bell (source of the "Art" quote). She is a bit smarter than most of the other characters in this trope, but still has a little too much air between the ears than is good for her.
In a Friends episode, Joey memorized details about all the artwork in a gallery, then messed it up as he got left and right confused.
And in another episode whilst writing a letter to an adoption agency, he uses a thesaurus to increase his vocabulary. Hearts become "Aortic pumps" and so on.
The Suite Life of Zack and Cody: London hires Maddie to help her pull Playing Cyrano on a hot merit scholar, Trevor. The plan backfires when Maddie can't restrain herself from getting into a debate over politics with him, culminating in a Slap-Slap-Kiss. Fortunately, London seems more confused than hurt.
The Doctor has been getting into trouble by pretending to be more knowledgeable than he actually is since The Aztecs in 1964.
Maxwell Smart from the Get Smart series did this all the time, to everyone. He didn't always have someone to help him feign competence either, and on those occasions got found out quite quickly.
The borderline mentally disabled Randy in My Name Is Earl seems to be really good at this, once befriending a bunch of business men, getting a job and earning a lot of money in less than a day with just the help of a second-hand suit.
Ted Baxter used to pull this one off with regularity - one instance in particular stands out.
Ted's son: Mother, I abhor you!
Ted: Now son, I'll have none of that language in this house!
In the iCarly episode iQ Carly tries to convince a very intelligent boy she wants to date that she's very knowledgable, via the internet, studying real hard and eventually cheat sheets just to bluff her way through a day.
Foggy Dewhurst from Last of the Summer Wine had more or less convinced himself that he knew everything based on the simple fact that he was Foggy Dewhurst. On one occasion, he convinced himself that he had to know what a "Loxely Lozenge" was simply because he existed and must've heard it at some point and simply needed to bring it to the front of his mind. He thought it was a cough drop. Turns out it was a very rare automobile. He then stubbornly tried to convince the others he'd been speaking in code in case others had been listening in, and while they weren't fooled, he managed to fool himself.
The oldest Steven sibling in Even Stevens is an airheaded Dumb Muscle jock. In one episode he decides to act smarter to impress people, and watches a video to this end that recommends wearing glasses and using big words. Towards the end of the episode he meets a woman wearing glasses; they hit it off when they realize they both watched the video and are playing the same "pretending to be smart" game.
In Black Books, Bernard attracts a girl by pretending to be a jazz pianist. Since he had Manny playing the chords from inside the piano with spoons, Fran gets back at him when she expands Bernard's lie to falsely out him as a genius:
Bernard: What did you say to Kate? She thinks I'm the Renaissance. She'll think I've lied! I have to go along with all this reclusive genius stuff — she's going to be very upset when she finds out I'm a reclusive wanker.
A man named Fantastic convinces the local government that he can repair a nearby power plant. When asked if he's studied theoretical physics, he says "I have a theoretical degree in physics". No one who's ever met him has fallen for his act, and killing him in broad daylight won't anger anyone else in the room, or in the game for that matter. You can even blackmail him into paying you so that he can keep his job since he needs to support his drug addictions somehow. If you manage to bring the plant back to power in favor of the NCR, he can be found in Hoover Dam later on as the "Goddamn Dam God".
Similarly, there's Ricky in the beginning of the Honest Hearts DLC, who brags about how awesome he is. With sufficiently high skills, you can not only point out how his Pip-Boy is broke, but that he's obviously a drug addict and how the details of his stories are completely inaccurate (for example, having an "11mm SMG" and having killed "Deathjaws"). You can either get him to scram or blackmail him into carrying more of your stuff.
Example: Starting to move directly towards the destination while scheduling the time consuming path finding for later.
In Star Control 3, the K'tang species tries very hard to look powerful and intelligent. They fail miserably at the latter.
In one Homestar Runner cartoon, Strong Bad tries to get Homestar to say something intelligent, even dressing him up with a lab coat, glasses, and a test tube. ("Check it out, Strong Bad, I look a-smart!" "You sure do, stupid.") However, Homestar managed to turn it around on him and get Strong Bad to say something stupid.
Thisxkcd comic indicates that there are some topics where you can get away with it.
This page of mezzacotta — yes, even pseudorandomly generated speech bubbles mock this pseudorandom garbage.
Simmons from Red vs. Blue is zigzagging with this trope. While he is the Unofficial Science Officer of the series and good with computers, he's also been stated to be less intelligent than he thinks he is and will abuse the fact that the people around him are either too lazy, stupid or insane to call him out on making stuff up.
Simmons: If you want me to multiply two big numbers in my head, that I can do.
Thisxkcd quote demonstrating what a politician trying to get away with knowing little outside of rehearsed "hot topics" can run into.
The Idiot Nerd Girl meme, although she feigns "geek cred" more than intelligence.
Homer Simpson chooses to wear a pair of nerd glasses that were dropped in the toilet by Henry Kissinger. Unbeknownst to Homer, Mr. Burns then assumes he's an egghead and decides not to fire him during a round of job cuts.
One of the reasons thought to have contributed to the ancient Greek philosopher Socrates' execution was that he went around pissing off people in power (such as politicians, and, more drastically, religious figures) off by asserting they were doing this.
There are known garbage texts that can pass as "scientific" in nonsense-rich environments and really made it to the respective journals or conferences... Including automatically generated ones. If you want to hunt impostor "scientists" in comfort using a robot decoy-duck—go ahead, it works.
Social Text published Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity article (It claimed to be about using quantum theories of gravity to stick it to The Man) which turned out to be a parody made of statements specifically designed to be a solipsist nonsense and logically disconnected claims. note They even managed to insult themselves further by rejecting an explanation text as not meeting their intellectual standards after publishing this mockery (it apparently didn't "Transgress the Boundaries" enough).Papers by Alan Sokal has a full story, papers and a simple recipe how to bake such a cake at will.
WMSCI 2005 accepted an article Rooter: A Methodology for the Typical Unification of Access Points and Redundancy, which is a pile of robot-generated garbage. Then guys went to that conference, held a "technical" session and with straight faces gave several more randomly generated garbage speeches. There's a story, papers, movie — and SCIgen itself, released under GPL.
Here you can get random Postmodernism texts online, and even permanent links note randseed-based, obviously to the particular essay, if you liked it.
Any agenda-based statistics study. I.e. if they're paid to prove a causal link exists instead of determine if one does, they will use this.
There is a psychological term for feigning intelligence. This is called illusory superiority and is a cognitive bias that makes people overestimate their positive qualities and abilities and underestimate their negative ones relative to others.
The Dunning-Kruger Effect is when "people reach erroneous conclusions and make unfortunate choices but their incompetence robs them of the metacognitive ability to realize it", or as Cracked.com phrases it: "a short cut in the brain that makes people suck at figuring out they suck." To test the Dunning-Kruger effect, two men named David Dunning and Justin Kruger ran a series of experiments and published the results in the Journal of Personality and Social Psychology in December 1999. What they found was that “ignorance more frequently begets confidence than does knowledge.” Specifically they concluded: (1) Incompetent individuals tend to overestimate their own level of skill. (2) Incompetent individuals fail to recognize genuine skill in others. (3) Incompetent individuals fail to recognize the extremity of their inadequacy. (4) If they can be trained to substantially improve their own skill level, these individuals can recognize and acknowledge their own previous lack of skill.