I'll Pretend I Didn't Hear That

There are times when an authority figure has to be flexible but still maintain their authority. In these times, many use the following tactic to make clear that they have noticed an activity by commenting on how they haven't noticed it. This way, they're able to draw attention to the fact that the activity is prohibited while still allowing it to happen.

This is not willful ignorance; the authority figure is making it known that they are aware of the situation but for some reason feel that drawing further attention to it might be a problem. This usually carries one of two messages:

"Sergeant: Go home, Private, before I have to notice you being drunk and disorderly."
 * 1: "I don't want you to be doing that, but I will give you one warning." Example:

"Sergeant: It's a good thing I can't see you doing that graffiti, Private, or I would have to report you to the C.O., no matter how much of a moron you think he is."
 * 2: "I want to turn a blind eye but also want to warn you not to mention it again because the next person who overhears might not be as sympathetic." Example:

A form of verbal irony.

See also Suspiciously Specific Denial.

Anime and Manga
"Captain Komamura: "Rest easy. Unfortunately, my ears are not working well today.""
 * Bleach: After overhea... sorry, NOT overhearing a conversation between Iba and Ikkaku.

Comic Books
"Gordon: You must be wearing some armor under that jacket. Bruce Wayne: Yes. Gordon: You know, I'm practically blind without my glasses. Sirens coming. You'd better go."
 * At the end of Batman: Year One, Gordon realizes that the man who just saved his son must be the same Batman who the Gotham Police have been hunting.

"Spider-Man: You could have turned it down! Daredevil: The judge would have asked why I was recusing myself. 'Well, your honor, in my secret identity as Daredevil, I'm friends with Spider-Man, and the defendant tried to kill him." Spider-Man: You could have lied! Daredevil: As an officer of the court, I'll pretend I didn't hear that, although since I'm literally capable of hearing a pin drop, that's a tough trick."
 * In the one-shot Trial of Venom comic, Spider-Man is understandably upset when he hears that Daredevil is defending his enemy Venom:

Literature

 * Dumbledore does this in Harry Potter and the Goblet of Fire, although in this case, Harry had already apologized for mouthing off against Rita Skeeter: "I have gone temporarily deaf and haven't any idea what you said."
 * Almost as if he were turning a deaf ear to Harry's apology....
 * Near the end of Holes: "I didn't hear that. And I advise you to make sure I don't hear it again."
 * Discworld:
 * In Monstrous Regiment, Sergeant Jackrum says to a sentry who has left her post, "I must have bleeding good eyesight because I know for a fact you are on sentry duty over by those trees."
 * In Jingo, Lord Rust doesn't have to pretend he didn't hear Commander Vimes call him an "inbred streak of piss", because Rust is so convinced that anyone beneath his station would never blatantly insult him that he literally doesn't hear Vimes.
 * Robert Heinlein liked to use this one.
 * In Space Cadet, when Tex Jarman gets drunk in public, one of the cadet's instructors (who is sitting nearby) calls over Matt Dodson and indirectly warns him to get Tex out of there before he has to take official notice of his drunkenness.
 * In The Number of the Beast, the protagonists ask the Governor of the UK colony on Mars how they can exchange their gold for the local currency. He offhandedly mentions how he is glad to hear they don't have any gold, being it is illegal there for individuals to own gold.
 * Starship Troopers has a strange variation. During basic training, a recruit strikes a drill instructor. Though the instructor—and later the base commander—do their best to ignore this, the recruit makes it impossible for them to do so (saying point-blank that he did it during a formal legal procedure). He's instantly court martialed, found guilty, whipped, and dishonorably discharged—which is actually a light sentence possible only through some deft legal maneuvering on the part of the commander, because striking a superior is normally a hanging offense.
 * In Betsy Byars's book The Pinballs, two of the child protagonists, Carlie and T.J., smuggle a puppy into the hospital to cheer up their friend Harvey. A nurse catches them doing this, but seeing that Harvey is genuinely feeling better thanks to the puppy, she tells them something along the lines of, "Now, you be careful with that puppy. Why, if I had seen it, I'd have to take it out of the room this very minute." Carlie is so impressed with the nurse's attitude that she declares later on that if she becomes a nurse, she'll act in the same way the nurse did.
 * Jack Aubrey does this on several occasions, usually when Stephen or Killick is muttering something that it wouldn't do for the Captain to take notice of.
 * David Sedaris writes that when his mother was dying of cancer, he tried to end a phone conversation with her by saying, "I love you," and she responded, "I'll pretend I didn't hear that."
 * In Jerry Pournelle's West of Honor, one of the lieutenants comes across a private painting graffiti on the orderly room wall. He simply points out how unfortunate it would be if the Sergeant Major had been the one to catch him, and says that he expects to see the wall clean when he returns. He also lets pass without comment the private's explanation that "IHTFP" stands for "I Have Truly Found Paradise" (rather than "I Hate This Fucking Place").
 * The Belisarius Series has a running gag with Valentinian; when the latter mumbles something, typically cursing about the situation Belisarius is leading them into, Belisarius (who knows exactly when is being mumbled), asks what was said and someone, typically Anastasius, will cheerfully repeat it out loud...but since it would be insubordinate for Valentinian to say something like that, it might have actually been something else that sounds vaguely similar.
 * In Star Trek: Vanguard, Captain Desai (the station's JAG officer) responds to a mission request by Admiral Nogura with something akin to accusing him of trying to punt her off the station to avoid legal trouble. Nogura replies that, as a favor and for the sake of her Starfleet career, he's going to pretend he didn't hear her insubordinate remark.

Live-Action TV
"Helo: They tried to live with us on New Caprica. Roslin: What did you say? Helo: They tried to live with us on New Caprica. Roslin: You weren't on New Caprica. To my recollection you never set foot there? So out of respect for the hundreds of men and women of your crew who suffered through that snakepit... I'm gonna pretend I didn't hear that."
 * At least two instances on Battlestar Galactica:
 * When Galactica stumbles across an infected baseship in which all the Cylons are dying after they encountered a probe containing an ancient plague, an opportunity presents itself for the Colonial Fleet to destroy the entire Cylon race once and for all. This could be done by taking a few still alive ones that they found on the ship, and then killing them after jumping in range of a Resurrection Hub, infecting the entire system with the incurable disease. Being himself married to the (good) Cylon Athena, Helo Agathon objects to it on principle when the Galactica command staf are discussing the option with President Roslin. Then this conversation happens:

"Reeves: Oh you cheeky so-and-so. Mortimer: I'll pretend I didn't hear that. Reeves: I can't blame you. (or "I'll pretend you didn't")"
 * After they bring up the subject of the Final Five Cylons (a taboo topic in Cylon culture) Cavil orders a number of his fellow Cylons to "take a cleansing walk" and he'll forget what he just heard them say.
 * Subverted in an episode of Bones. Bones told Caroline Julian (the DA) something and Julian said "I didn't hear that," so Bones started to repeat herself louder.
 * In an episode of Ned's Declassified School Survival Guide, a character starts an underground reaction to the school talent contest and one of the other characters asks the woodwork teacher for advice. His reply goes more or less "I, of course, didn't hear you refer to an event that the principal has specifically prohibited."
 * On That '70s Show, the main characters are talking about sex using thinly veiled metaphors, until Mrs Foreman complains: "You're making it really hard to pretend I don't know what you're talking about".
 * Jim Keats, the season 3 Big Bad of Ashes to Ashes is hardly a Reasonable Authority Figure -
 * Happens somewhat regularly on both NCIS and NCIS: Los Angeles. Either the team needs something but don't have the time to get approval or approval would tip off the perp or Gibbs/Vance/Hetty require plausible deniability.
 * On Hogan's Heroes, Sergeant Schultz frequently said "I see nothing!" because he knew that investigating would just make things worse for him.
 * A recurring exchange in the first season of The Smell of Reeves and Mortimer, whenever Mortimer tells a bad joke:

Video Games

 * Inverted in Final Fantasy X. Devout Yevonite Wakka questions the involvement of Maester Seymour Guado - essentially a high priest of Yevon - in an operation that uses machines forbidden by that religion; Seymour coolly suggests he simply pretend he doesn't see them. When Wakka, shocked, protests that that's not something a Maester should say, Seymour replies, "Then pretend I didn't say it." This is one of many early clues that Seymour is Obviously Evil.
 * In Company of Heroes, a cutscene shows a sergeant chugging away on a bottle of french wine. An officer strolls up and says he'll "assume that's grape juice". The sergeant says as the officer walks away "Right sir, grape juice! Well, it was...'bout a year ago."
 * Mass Effect 2 - If you have Grunt in your party when you enter the quarantine zone on Omega, he'll ask if the smell of burning corpses makes anyone else hungry. If you also have Jacob, he'll drop the line.

Web Animation
"Ozpin: I'm still curious how you all found yourself at the docks last semester. I'm interested to know how you really learned about a hideout in the southeast. And I certainly wonder why witnesses reported seeing robots and rose petals in a dance club some time ago. Ruby: Um... well... Ozpin: I doubt I'll ever find the exact answers I'm looking for. So how about this: instead of waiting for you all to break the rules, why don't we just bend them?"
 * Ozpin did this in RWBY, Volume 2, Chapter 8: "Field Trip".

Western Animation
"Aang: I'll pretend I didn't pretend to hear that."
 * Avatar: The Last Airbender:


 * When Marge of The Simpsons becomes a police officer, she offers to turn a blind eye to Homer buying beer for teenagers as long as he moves his car away from where he's parked it across three handicapped spaces. He doesn't, instead opting to take her hat and do a mocking impersonation of her, so she arrests him anyway.

Real Life

 * Someone demonstrating a home-made flame thrower was approached by an off-duty cop and informed that had he been on duty, the officer would have had to arrest the user for having a weapon of mass destruction. The user immediately yanked the fuel supply out and both pretended that it was a lighter.
 * In Wikipedia it's a written rule. On the user level, offenses are excused for the first couple events without penalty, and those first couple events can happen many times if spaced far apart. On the article level, they have a number of rules and even a pillar saying in almost as many words "If it sounds right, it doesn't have to follow the rules." If we don't like what you're saying though, there are no shortages of rules and clauses it can be attacked with.
 * All The Tropes has a similar practice -- according to our guidelines for applying bans, being disruptive on a one-off basis is not grounds for any kind of a ban because "everybody has a bad day once in a while".