Most of the humor derived from the Pirate Court scene in At World's End.
An infamous deleted scene from the first Star Wars movie shows Han Solo, Luke Skywalker, Chewbacca, and Princess Leia strolling through the corridors of the Death Star, their faces uncovered and their street clothes clearly visible, but also conspicuously sporting some stark white utility belts they have stolen from Imperial stormtroopers they've knocked out and/or killed; all in full view of the Imperial personnel! Apparently, the only explanation is that Han, Luke, Chewie and Leia figured that the enemy would find this sight so funny or brazen or unbelievable that they'd dismiss it. (One theory is that George Lucas shot this scene for no other reason than to add to his personal blooper reel.)
American Gangster: Lucas shoots a man who owes him money in broad daylight, then resumes eating dinner on the same block.
Back to the Future: When Biff and his sidekicks chase Marty on the impromptu skateboard, and they approach the manure truck, Marty climbs over their top-down car, through the sidekicks, and lands back on the skateboard.
Be Kind Rewind: When every tape in a video rental place is erased, the leads decide to do 20-minute no-budget versions of the films themselves and hope nobody notices. It didn't work, but customers found the remade films had their own oddcharm, and the store was more successful than it was before the accident.
Big Fat Liar. Like any director would steal a creative writing assignment from some kid's backpack and turn it into his next big movie...
The 1987 Dragnet movie has the Turn In Your Badge moment as the result of the arrest of a reverend, like anyone would believe that he was organizing a drug rave and trying to offer a woman as a human sacrifice.
The crazier and more over-the-top the actions of the main characters in the movie Fear and Loathing in Las Vegas became, the more likely they were to get away with them. These actions included doing enough drugs to kill a herd of elephants, destroying their hotel rooms, trashing a couple of expensive rental cars, feeding a young girl with acid for a few days, waving around a gun and a knife while twisted, and showing up stoned out of their minds at a police anti-drug convention. The trope was invoked by Raoul Duke at one point, after a truly astonishing sequence wherein he and his attorney chase a pair of cops and their wives down a highway, demanding that they be allowed to sell the cops drugs; the attorney wonders if they'll be arrested, to which Duke points out that nobody would believe the victims if they tried to report it. The scary part is that this is based, however lightly, on actual occurrence.
"It was all over now. We'd abused everything that Vegas lived by; Burning the locals, abusing the tourists, terrifying the help. The only chance now, I felt, was the possibility that we'd gone to such excess that nobody in the position to bring the hammer down on us could possibly believe it."
The author Hunter S. Thompson's reputation is based on Refuge in Audacity. Stories circulate of him intentionally invoking this trope; when his house was found to contain over thirty firearms from handguns up to machine guns, and several sticks of dynamite, Hunter told the police that they were "for home defense."
Ghost: When Whoopi Goldberg's character signs the million-dollar check, she goofs and apologizes, "I signed the wrong name."
Indy's encounter with Adolf Hitler. When you're carrying a diary about the Holy Grail, which Hitler seems to want for some reason, and you come face to face with the man himself, do you hide it? No. You take advantage of the book signing you're at and get Hitler's autograph.
While escaping from Berlin in a Zeppelin which hasn't taken off yet, Indy notices an SS officer searching for him and his father. With no place to run or hide, Indy decides the best course of action is to disguise himself as a steward on the Zeppelin, follow the officer around, then hit the officer with a sucker punch when the officer finds Jones Sr and throw the officer out a window. The real audacity comes when Indy explains "No ticket" to the shocked German passengers in clear American English. The other passengers immediately present theirs.
In the Indiana Jones and the Last Crusade adventure game, you also can encounter Hitler. However, you are then given control of Indy and can give him a few different things to sign: the diary, a copy of Mein Kampf (you can give it to a guard at a security checkpoint), or a pass (which lets you go through any security checkpoint without problems). You can also punch Hitler but his bodyguard will make sure you don't live to enjoy it.
In Just One of the Guys, a teenager pulls a Sweet Polly Oliver so she can write an article about life as a guy. When her vacationing parents phone home, her brother informs them that his sister has become a transvestite, and is assumed to be kidding.
Mr. Banks: Will you be good enough to explain all this? Mary Poppins: First of all, I would like to make one thing quite clear. Mr. Banks: Yes? Mary Poppins: (brief pause as if tongue-tied, then wavering slightly tearful, fast tone) I never explain anything.
Julie Andrews's rendition of that line may have made it a subversion, aversion, or justification. She doesn't say it in her usual firm, no-nonsense statement of absurdity.
Cardinal Richelieu: Ah, yes. That is usually the first. Let me see if I remember it correctly. While the English attack from without, the wicked Cardinal undermines from within, forging a secret alliance with Buckingham and placing himself on the throne. But really, Your Majesty, why stop there? I have heard much more festive variations. I make oaths with pagan gods, seduce the queen in her own chamber, teach pigs to dance and horses to fly, and keep the moon carefully hidden within the folds of my robe. Have I forgotten anything?
These lines are delivered in Tim Curry's delightful sneer, from which anyone Genre Savvy should run like the wind.
In Leap of FaithThe Protagonist gets out of a speeding ticket by cold reading the police officer and taunting him about his divorce until he gets arrested. He then talks the cop into reconciling with his estranged daughter, and walks away a free man.
In The Men Who Stare at Goats the covert psychic organization is so outrageous, (has pseudo-hippie philosophy and refers to its members as Jedi) that the film can get away with harsh social commentary on the Iraq War that would otherwise make it controversial. The fact that the movie's based on real research the military actually engaged in makes it even more awesome.
In Once upon a Time in Mexico, Sands walks around wearing a CIA t-shirt (which reads "Cleavage Inspection Agent" in smaller letters underneath). This in itself isn't weird, but then you remember that he's a reall CIA agent.
The ending of Teenage Mutant Ninja Turtles II Splinter's reaction not withstanding. Consider, four mutant ninja sewer-dwellers duking it out with two super-mutants and a squad of ninjas, in a dance hall, to an impromptu rap song by Vanilla Ice, who then proceed to toss high-fives to the crowd, then hop onto the stage, perform dance moves and shout "Give it up for a Turtle!" None of the people there find this weird. Instead, if their reaction was any indication, they thought it was All Part of the Show (if unusual for a hip-hop performance).
The parade. Joker preempts the Mayor's television address to the city with his own broadcast, and then - after having shamelessly killed dozens of people in the cruelest way imaginable - announces that he is going to hold a parade in the center of town and toss 20 million dollars down to the spectators if they will show up - and they do.
The Riddler uses his technologically enhanced intelligence to locate Two-Face's hideout and then storms in there without invitation. He proposes that he and Two-Face join forces in a scheme to unmask Batman. Two-Face points out that "violating the sanctity of our lair" is an abomination and to attempt it is foolhardy, but he's intrigue by the idea enough to toss the coin on it. If it had come up "bad heads" he'd kill Riddler. It didn't
Die Hard With A Vengeance features John McLain walking around Harlem wearing a sign that proclaims "I Hate Niggers" (the Big Bad made him do it). The street corner at which John is forced to stand is less than twenty yards away from the favorite hangout of a street gang armed with knives. Zeus Carver ominously lampshades this - not five seconds before said gang members spot the sign and come over looking for trouble, and one of them hurls a switchblade that lodges in the sign. John quickly tries to save himself by pretending to be a religious fanatic....which doesn't work. What's most outrageous is that John and Zeus both survive this harrowing encounter with little more than a beer bottle broken over John's head and minor knife wound for Zeus.
Weekend at Bernie's. Two ambitious young men, hoping to climb the corporate ladder, are invited to a weekend long bash at their boss Bernie's beach house, not knowing that a scam they recently uncovered is Bernie's doing and that he plans to kill them. Then Bernie himself is killed by his own hitmen, and the two protagonists try to extricate themselves from the situation by making the guests believe Bernie is still alive, even when his corpse is in plain view.
Jingle All the Way: When Arnold is caught in the bootleg toy warehouse by the cops he grabs a toy police badge from an open box and bullshits like his life depends on it to convince the cops he's an undercover detective. This moment seems more audacious when you remember that impersonating a law enforcement officer is a serious crime in the United States. Had his bluff not worked he would have gone to prison for a long time.
In 48 Hrs., Murphy intimidates an entire redneck bar with nothing but his own bravado and Nick Nolte's borrowed police ID, which he flashes while covering the photo.
As Axel Foley in Beverly Hills Cop, he pulls the same stunt repeatedly, flashing his Detroit cop badge rapidly while pretending to be a customs officer, a foreman, etc.
He also manages to get himself a luxury suite in a posh Beverly Hills hotel by claiming to be a Rolling Stone reporter and threatening to write an article claiming the hotel was racist because the "lost" his non-existent reservation.
In The Golden Child, there's a scene where he pretends to be some kind of Federal Agent, and flashes what should be his badge around...if he actually had one on the part of his wallet that his hand is covering.
Outbreak: in order to get to Cedar Falls, Dustin Hoffman's character — a Colonel — comes stamping into the aircraft dispatcher's office demanding to know why he isn't on the passenger list for the next flight to the town. (He's been ordered not to attend.) Variously demanding the dispatcher call his superior officer and then not call his superior, Hoffman gets onto the passenger list and flies because he's intimidated the dispatcher into authorising him.
The climactic battle of Fifty/Fifty has Jake Wyer and Sam French pinned down by the Tengaran army. Then Jake says he has a plan:
Sam: Alright, what is it?
Jake: Full frontal assault.
Sam: That's your plan? A full frontal assault is your plan?
Kentucky Fried Movie has "Rex Kramer: Danger Seeker!" who, after dressing up in typical daredevil attire, goes into the middle of a group of black men in an alleyway, shouts "NIGGERS!" and runs off. The sheer ridiculousness of it makes the men stand around looking at each other, giving Rex a 2 second head-start.
In The Lady Eve, a millionaire throws over his fiancee when he learns that she's a notorious con artist. Her revenge involves showing up at his mansion under a different persona and re-seducing him - which works despite her not putting on any kind of disguise whatsoever. She has correctly predicted that he would conclude that, had it really been her trying to fool him, she surely would have changed her appearance in some way; in other words, she looks too much like herself to be her. (It helps that she knows this particular man to be the most gullible chump on the face of the planet.)
Both in and out of universe in Star Trek IV: The Voyage Home. The film crew tested the plausibility of Kirk and company walking around San Francisco dressed like people from the 23rd century by dressing staff in the characters' costumes and having them walk around San Francisco. Nobody gave them a second glance. In the movie itself—with the exception of Chekov—the former Enterprise crew got away with being profoundly weird, with no consequences.
Hong Kong actor Stephen Chow uses the Mo lei tau comedy style in many of his movies, which in turn relies on this trope.
This is the modus operandi of most Bond villains. Goldfinger convinces multiple crime syndicates to help him rob Fort Knox with the argument that no one will be expecting it.
In Arthur (the 1981 film), Linda Marolla steals a necktie at Bergdorf-Goodman's. The store detective witnesses the theft and follows her out into the street, where he confronts her. After making a snarky comment, she goes on the defensive, pretending she is some kind of official, pulling out a pad and pencil and demanding the detective's name and address. When this fails to intimidate the detective, she yells for someone to find her a cop, at which point Arthur steps in and saves her bacon.
"Statistical fact: Cops will never pull over a man with a huge bong in his car. Why? They fear this man. They know he sees further than they and he will bind them with ancient logics."
G.I. Joe: Retaliation: How do you push for full denuclearization? Launch all your missiles, get the other guys to launch theirs, then abort the launch to get the others to do the same. Bam! Nukes gone.
In Now You See Me, for their first show, the Four Horsemen rob a foreign bank from Las Vegas. When they're arrested, Daniel rightfully points out that they can't very well make the charges stick unless they're willing to admit magic is real. By the time they have an idea of how the Horsemen pulled it off, they've already been forced to release them and still can't actually prove their theory.
Pain and Gain: The other reason the police don't believe Kershaw at first. As Ed says near the end during the trial, "sometimes truth is stranger than fiction".