Tiberium Wars has this happen multiple times. In fact, half of Havoc's plans involve them being so ridiculous no one sees them coming, and in Chapter Fifteen, the ruined remains of Lieutenant Wallace's Zone Trooper squad attacks hundreds of Nod soldiers, tanks, beam cannons, and Avatars.
Five Score, Divided by Four: The Feds and the cops are on high alert after a seeming terrorist bombing in Seattle. How do five technicolor mythical equines manage to get out of Seattle and halfway across the US? Charter a private plane and a limo, of course.
In First Knight, a Slayer was in the middle of a debate while running for sheriff when she realizes her opponent is a demon that feeds off negative emotions. After cutting off its head in front of the crowd, causing lightning to shoot out due to built-up energy, she plays it off by saying, "There can be only one."
In Origins, a Mass Effect/Star Wars/Borderlands/HaloMassive Multiplayer Crossover, Admiral Nimitz's only safe spot is here. She claims that the Trans-Galactic Republic does not condone torture (directly or by proxy), but then hands a prisoner to a group that's known for its love of unaccountable secret agents whose actions can be washed awaynote The Citadel Council generally throws up its hands if its Spectres or other similar persons misbehave. When called on this, she cites the treaty that theoretically set this all up, resulting in a pile of Loophole Abuse/Half Truth/False Reassurance all in one!
In Water Under the Bridge, the Blue Gloves send an agent with no infiltration skills to infiltrate Serenity just as a reminder that they have their eye on the crew. They agent they send is so obviously an infiltrator (including telling them she's going out of her way to become indispensable and wearing her Blue Glove uniform) that the crew never suspects she's a Blue Glove.
Weiss Reacts: Blake is the best example, among other things taking a universe-shattering mecha for a joyride, but Cinder pulls this off by accidentally blowing up several cars that double-parked in front of her while she was attempting to buy burritos, and then proceeding to run across the roofs of Vale in a domino mask while clutching said burritos and being pursued by a veritable army of robot soldiers.
In Origin Story, Alex Harris's response to the Runaways showing up to interrogate her is to pick up Bruiser and carry her to the buffet she and Louise were already heading to. Alex and Louise ignore any attempt to talk until they're both sitting at a table, plates full of breakfast foods in front of them.
In DC Nation, this is the standard operating procedure of Travis Grey (an Original CharacterGreen Lantern). A street kid and pickpocket, he steals Hal Jordan's wallet and spare ring. After donning the ring, he proceeds to go on a one-man cleanup spree through his rough New York neighborhood. He tops it by making a Sarcastic Confession to Guy Gardner and Hal about his activities, chiding Hal to keep better track of his stuff, and all but daring the two veteran Lanterns to steal the ring back. Hal's ticked, but Guy's about to double over laughing.
In The New Guild, Sandra Battye picks up an hitherto lost and unclaimed title for her Trade Guild. She cannot use the appropriate title because another, larger and more powerful, Guild has pre-empted her. Against Mrs. Rosie Palm's vigorous objection, Lord Vetinari grants Sandra title to the name...
In Magical Relations, one of the myriad "Harry Sorted into Slytherin" fanfics, Parseltongue is a teachable language. Naturally, Snape offers to tutor Harry in nonverbal magic, dueling, Occlumency, etc. for as long as it takes Harry to teach him to speak snake. Eventually, Harry is learning Leglimency to improve his Occlumency (highly illegal without Ministry permission, not that they care), but now The Umbridge is around to poke her nose in. Snape first tries to cover up the lessons by giving Harry detention, but when Umbridge shows up to watch the private, Headmaster-approved lesson anyway, they treat it like business as usual, and Snape starts quizzing Harry on his Occlumency reading in Parseltongue. When Umbridge demands to know what language that is, Snape tells her that it's naturally the Ancient Mayan Wizards' language of Uspantek, because Harry is aiming for a job as a cursebreaker, and the only way to learn a language is through practice (naturally, Umbridge will be less than familiar with either language that has only a handful of living practitioners). When Umbridge eventually demands that they speak in English, Snape starts quizzing Harry on his advanced Arithmancy (for curse-breaking, which he has never taken), and subtly prompts his student to Leglimens the answers from his head. (Which is, again, highly illegal).
Snape:(in Parseltongue) Excellent. I will take your essay after this saggy, cloying excuse for a dictator leaves us.
Harry:(one scene transition later) So then I answer questions about advanced Arithmancy for the rest of the lesson, and when we're done, Snape looks at Umbridge and says, 'Thank you for your time. Your presence tonight has been invaluable.' (looks at his friends with wide, despairing eyes) It was madness.
In the same fic, Harry & Co defeat the Basilisk using Ron's experience handling roosters. They could go to a teacher about the dead giant snake in the girls' loo... or they could hang an "Out of Order" sign on the door and turn the place into a lab for harvesting the thing for extremely valuable potions ingredients. After all, they killed the thing, and have as much a right to it as anyone. By the time they report it to Snape, they've already harvested the blood and are starting on the fangs and skin, and they offer him the extremely invaluable eyes in return for endorsing this stunt and giving them any pointers. This is deemed an... adequate... payment, and when the professor sees their organized, efficient system, he turns the eye extraction into an impromptu potions lesson.
Pansy:(after Snape's departure and a quick stunned silence) That went surprisingly well.
During the Chunin Exam in Reaching for a Dream, Naruto cheats on his test by punching out one of the Chunin plants and taking his test.
In later stories, Naruto and Xanna don't bother hiding their horns, claws, or slitted pupils and simply act like there's nothing odd about having them. Of course it helps they're in Japan and most people simply assume they're cosplaying.
In Cheaters Prosper Naruto does something similar: he walked up to Kabuto, took his answers and left him his own blank sheet. Then he gets the team to pass the second part of the test by swiping the other necessary scroll before the start of the test, sealing the tied-up Sasuke and Sakura in a scroll, and transforming himself in a needle stuck to Anko's foot, resulting in the examiner carrying the whole team past the test.
I Am NOT Going Through Puberty Again! has time travelers Team 7 and Hinata not even bothering to hide their remarkable increase in skill. The Hyuuga Clan simply believe that Hinata finally snapped from all the pressure, while Kakashi rules out his team as potential spies, as any infiltrator capable of replicating Naruto's seal or Sasuke's spinny eye of doom would be outright retarded to show off their strength so blatantly (Sakura is ruled out by association).
Naruto makes Kankuro and Temari think they're being detained by Anbu in Naruto: The Gamer Files to make them release Konohamaru. It helps that trying to harm a Kage's family would result in such a reaction.
Sonic X: Dark Chaos: Maledict secretly controlling the Metarex using an incredibly poor disguise was basically this, and the only reason it worked was because neither Dark Oak nor Tsali could believe that Maledict would be able to pull it off.
Basically everything Eric the Hedgehog does or says is this. Discovering that Molly and Leon's refugee group are eating their dead? Ask for dessert. Taking on an entire Demon fleet led by Satan himself? Charge in guns blazing and ram Maledict's flagship while blasting the 1812 Overture over coms. Indeed, it's said in-story that the reason he's so dangerous is because he literally has no concept of fear.
Strange Times Are Upon Us: Ila'kshath's answer to Brokosh complaining about him talking to a 19th century American boy. (Ila'kshath, a Gorn, was hunting the same deer as the kid, got seen, and said, "Blink, boy—your eyes are stuck!" The kid fainted.)
“Who’d believe it? Seriously, think about it—a giant reptile that talks? He’d be laughed out of the room before he got three words out.”