I had the right to remain silent...but what I lacked was the ability.
— Ron White
Someone lets something slip that reveals plot-sensitive information to another character. Sometimes this is a pure accident, to move the plot along. Sometimes this is the result of the protagonist pulling an Exasperated Perp.
In a non-crime-related plots, it's used to create dramatic or amusing conflict.
Ookami-san gives us a moment, as well. After her bout with Easy Amnesia, Ryoko is walking home with Ringo. Ryoko informs Ringo that she doesn't remember anything from the time where she had regressed to her younger self. When Ringo asks Ryoko if she's hungry, Ryoko tells her she's still full from the parfait she ate. Except she ate that parfait during the time she claims she can't remember. Ringo quickly realizes that Ryoko does indeed remember, and uses that information to blackmail her into wearing a cute little ribbon in her hair.
In the Alabasta arc of One Piece, Igaram says aloud that the royal guard currently fighting Sir Crocodile have used a Deadly Upgrade and will die shortly. Crocodile overhears this, and retreats to a rooftop to watch them die uselessly.
CP 9 agent Fukurou, in spite of having a giant zipper over his mouth, tends to blab intel to the enemy. The mission before the Enies Lobby battle was complicated by his jabbering, and the Straw Hats were able to plan their rescue of Robin thanks to his 'hints.'
In the Arlong Arc, Nezumi accidentally reveals that he's working for Arlong to prevent Nami from earning enough to fulfill her end of the deal to buy back her village this way. When he and some Marines come to confiscate her treasure stash and they're having trouble finding it, he yells that they're specifically looking for 100 million Berries, the amount that Nami was supposed to give to Arlong (although she is a few million short as of their arrival). Nami immediately realizes that Arlong was the one who informed them.
Happens many, MANY times in Detective Conan, whenever the culprit is confronted.
In the Ace Attorney manga, Turnabout Showtime features an example in which it is not revealed that the person has made a mistake until very late in the trial. Raymond Spume yells at Julie Henson for "biting her nails during the show just like (she is) now!" when pulling the murdered Flip out of his costume. It turns out that Sparklestar's (the mascot Raymond plays) back was turned to Julie while she was biting her nails, meaning that Raymond could not have seen her doing it unless he was wearing his costume backwards, which would enable him to unzip it and stab Flip, who was also wearing it the same way so that he could perform a backflip the same way he did a front flip.
Kenichi: The Mightiest Disciple gives us Rimi, also known as the Yomi-member Atlantis. She tends to blab otherwise confidential things when she first appears, including what she's doing.
In Bakuman。, Nanamine, who is working with a group of online consultants changed the first chapter even though his editor was fine by it. When Kosugi, his editor, asks about it, he says "You might have been satisfied with it, but everyone else wasn't." Kosugi then realizes what's going on and Nanamine shows him his plan.
Played with in Death Note. L tries to get Light to mention something that only Kira would know, only for Light to know this from the start and carefully avoid saying anything. However his skill at doing this just makes L more certain that Light is Kira.
In the Girls und Panzer "Little Army" manga, after Chihiro sprains her ankle, the group of herself, Miho and Hitomi needs a driver to get home. At this point, they see Emi, who is on her way home, and who starts to leave, offering to call for help. Miho then points out that, based on some of Emi's earlier statements indicating that she knows German tanks are strong and her identifying the tank type moments before, she knows much about driving a tank, and can drive. Emi sheepishly says that she "said something stupid like that without realizing it".
In Gotham Central, as a result of having been working long hours and being generally tired and depressed, Renee Montoya accidentally lets slip to Maggie Sawyer, captain of the Major Crimes Unit, that Romy Chandler had her weapon taken by Batman after she tried to shoot him.
Marcus Driver: "What, you figure I should just shoot over to this Tailor's place, get myself a Batman costume? Dress up and try to make Dunning wet himself?" Josie Mac: "Yeah, on second thought it's probably not such a good idea, Romy might try to bust a cap in your ass." Renee Montoya: "Yeah, well, he'd have to give her weapon back, first." Maggie Sawyer: "What was that?" Renee Montoya: "Oh, Hell."
It ends up being a crucial plot point in L.A. Confidential - a corrupt cop reveals that he's actually the murderer of a police sergeant by asking his subordinate Exley to investigate a name the sergeant dropped as his last words. Which happens to be a name made up by Exley for his father's unknown murderer; he'd told the story to the sergeant on the previous day.
Nini: (to the Duke) I don't like this ending. Why on earth would she go with the penniless writer? Oops! I mean sitar player.
The second one comes as a response to this:
The Duke:' Why shouldn't the courtesan marry the maharajah? Christian:Because she doesn't love you! ...him. She—she doesn't love him.
The first example is a deliberate leak, while the second is accidental.
In Two Days In The Valley, Teri Hatcher has hired killers to murder her husband. One of the police detectives notices that she says, "They killed my husband," implying that there were multiple murderers when the police hadn't established this fact yet. His partner brushes it off as a figure of speech.
Frau Hoffner: Come along, child. The auction is about to begin.
Mata Bond: Auction?
Frau Hoffner: Tonight we are selling one of the finest art collections in Europe.
Mata Bond: Le Chiffre's collection?
Frau Hoffner: Who?
Mata Bond: Le Chiffre.
Frau Hoffner: Who is Le Chiffre?
Mata Bond: The man who owns the collection.
Frau Hoffner: What collection?
Mata Bond: The collection that's about to be auctioned.
Frau Hoffner: Who said anything about an auction?
Mata Bond: You did.
Frau Hoffner: Who am I?
Mata Bond: Frau Hoffner.
Frau Hoffner: Never heard of her. You are insane, my child, quite insane.
Mata Bond: I think she's right!
The Djinn in the first Wishmaster film disguises himself as a friend of Alexandra, and comments that Alex's boss would really like her apartment. Alex notes that she never mentioned who she worked for. The Djinn manages to talk his way out of it.
In Kiss The Girls, Kate first starts to suspect that she's alone with the killer when he knows where her colander is without being told. He then proceeds to discuss in detail what kind of information a bad guy could get by going through her trash, before finally dropping pretense altogether to tell her exactly what he discovered when he went through her trash.
In Isaac Asimov's story Galley Slave a professor sues US Robotics, accusing a proofreading robot of altering his work. When the robot testifies, the professor blurts out "Damn you, you were instructed to keep your mouth shut about..." Oops. He had made the changes himself, then brought the case to make a point against automation.
The real twist is that the robot wasn't going to tell the truth anyway, since the First Law (manifested as a desire to protect the professor's reputation) trumped the fact that it would be scrapped if it didn't speak out, as well as the order to be quiet. The only reason for US Robotics' lawyer to call the robot to testify was in order to trick the professor, who distrusted robots and was deliberately ignorant of how they worked, into making that slip.
Poor Hagrid is prone to this, especially when he's distraught or talking to the Power Trio. He lets slip the means to calm Fluffy the Terrible, the name of a warlock who helps immensely with a search he doesn't want them to succeed in, and several other pieces of relevant information over the course of the books. Often lampshaded by Hagrid himself immediately after: 'I shouldn't have said that'.
Moist von Lipwig fell into this trope in Making Money when he was attempting to talk his way around Captain Carrot's Exasperated Perp tactic by telling Carrot that he knows what he's trying to do to him. Carrot then promptly thanked him... for informing him that he's quite familiar with that tactic and thus implying his rather shady criminal past. Whoops!
In The Diamond Age, Inspector Chang returns Hackworth's top hat, saying that he got it from a suspect. Hackworth thanks Chang for having "arrested him" despite Chang not having mentioned anyone being arrested, inadvertently admitting that the hat was stolen from him. He had wanted to keep the theft a secret, because the thieves had also stolen from him an illegal copy of the Primer that he had made.
In the Commonwealth Saga short story "The Demon Trap", Paula Myo is investigating a terrorist who has not only had his memories wiped, but a completely different set of memories implanted, but still proves his involvement because of a DNA match at the scene, and a mismatch where the person whose memories he has was sick. The head of the political party with the same aims as the terrorist group denies any involvement, but decries punishing a man for a crime his current personality didn't commit. In the process he describes the stewardess in sufficient detail to convince Myo that he provided the fake memories. It eventually transpires the entire movement consists of genetically-altered clones with a Hive Mind.
In Douglas Hulick's first novel, Among Thieves, the main character, Drothe has been tracking down a powerful book that's been rumored about, but which nobody has much information on, for his boss, Kells. Eventually he finds it, but when Kells asks what he's found, he tells his boss that he's not going to give him any information about "that damned journal" until Kells tells him what's going on. Kells realizes he's found the book, as everyone else has just been calling it "the book": nobody else knew it was a journal specifically.
In Daughter of the Lioness, Aly is keenly aware of this trope and tries very hard not to fall into it, which is difficult when Dove and Sarai are specifically asking for stories about legendary Tortallan figures who are part of Aly's family, like her mom and Daine the Wildmage. She also has to work hard to avoid sounding as well-educated and astute as she really is, but Dove still notices every time Aly slips up.
Knox: I don't just care about Fred - I practically worship it.
Gunn: You said "it".
Gunn: "Not "her". You said "'I worship it".
Knox (smirking): Oops.
In this context, "it" refers to the goddess Illyria, about to be reborn via the sacrifice of our beloved Fred. Fred is the "her". In this case, Knox believes that only Fred was worthy to be Illyria's host.
Stephen: If [the main character] went anywhere near the theater department, the football team wouldn't join him in a peppy dance number! They'd string him up on a goalpost by the tights of his home-made Romeo costume, and chuck stale Tater Tots at his head until I wet my pants! - his pants, his pants!
Another example, after 'Papa Bear' Bill O'Reilly appeared on his show, Colbert showed a clip of the O'Reilly Factor the next day where Bill says "Colbert blew me right away." Cue rant from Colbert how this was supposed to remain secret, how heartless O'Reilly was and it wasn't right away, they had dinner first. He goes onto his next segment where he uses the same phrase and realizes what Bill meant.
Stephen: Oh, my. I have misjudged him. And perhaps said too much.
This was common when he was on The Daily Show, too. Several installments of "Even Stevphen" ended with him and Steve Carell having turned the topical "debate" of the day into a thinly-veiled or not-at-all-veiled discussion of their personal lives.
Jack: Lemon, we have a problem. Liz: I have this whole Tracy-Josh thing under control! Jack: What are you talking about?
In Red Dwarf, Lister is reading Rimmer's diary to the Cat. Rimmer is outraged by this betrayal of privacy, and Lister tries to mollify him by saying he can read Lister's diary if he wants.
Rimmer: Why would I want to read your diary? It's full of puerile nonsense about Kochanski. Lister: Ah, so you have read my diary.
Law & Order: UK: During the prosecution of an accused rapist/murderer, the key witness is a young woman who saw the man lurking around the building where the crime took place (she may very well have been the intended victim had she not evaded him). The man denies it, angrily accusing the girl of lying and referring to her tattoos before covering his mouth in horror as he realizes his mistake. Although the girl's arms were indeed covered with tattoos, she was wearing a jacket while in court. The only way he could have known about her tattoos was if he had seen her previously.
Cuddy intentionally says too much to Wilson in an episode of House. She and House kiss, after which Wilson tries to trick her into confessing by asking her if everything's alright in a sort of leading tone of voice. She sees through the ruse and has no intention of denying the incident.
Cuddy: Everything's fine with my kissing House, oh God, you dragged it out of me, you're a genius.
Supernatural - Castiel eavesdrops on Dean, Sam and Bobby arguing about their suspicions that he's working with Crowley (he is). Bobby suggests that if there's any chance they're dealing with "a Superman who's gone dark side", it's a good time to stock up on Kryptonite. Later, after Castiel convinces them they were wrong about him, he makes one fatal mistake.
Castiel: It is a little absurd, though. Superman going to the dark side...
On Community, Troy has a tendency to do this, adding "Whoops" without changing the tone.
Troy: How do you know it was our design? We submitted in anonymously. Whoops.
In Castle's pilot, the brother of one of the victims, when asked about an alibi, provides alibis for the three murders. Castle feels downhearted, but Beckett points out that, while it is possible he'd know his alibi for his sister's death, the fact that he was prepared for all three murders is quite suspicious. He did it.
In the DoctorWho episode The Unicorn and the Wasp. The Doctor is trying to solve a murder mystery. Accusing everyone in the room about certain facts that could point towards them being the killer. He points to one man who is wheelchair bound. Who in turn cracks under the pressure and admits that he can walk and was only faking being paralyzed afraid that that was the only thing holding his marriage together. The Doctor then admits he wasn't actually going to confront him about anything.
Near the end of Persona 4, after guessing out the identity of the killer, the Investigation Team go to the hospital to interrogate him. While he initially tries to give off some basic and non-specific answers, the continued grilling from the team (and Detective Dojima) gets him to blurt out:
Tohru Adachi: "Namatame was the one who threw them in!"
In the 1st Degree. If you play the game right, Tobin will end up blurting out information that makes him guilty right there in the courtroom.
In Catherine Thomas Mutton assumes that Vincent has figured him out and accidentally confesses his involvement when he was never under suspicion in the first place.
Occurs in Suikoden V after the battle between Barows' army, Godwin's army, and the Armes army. Salum Barows feigns ignorance about Armes being there even though he arranged for them to be there. Then, Euram Barows runs in and practically confesses that they were working with them. Then, he goes a bit further by suggesting using the Dawn Rune which up until then had been thought to be in the hands of the village of Lordlake.
In Prince of Persia: The Two Thrones, the Prince, obsessed with finding and killing the Vizier, hears a woman scream, and heeds the advice of his dark half to keep going. Farah asks him if he heard it and he says that they should continue, because he is "sure she will be all right." Naturally, Farah realized he heard and is outraged, resulting in him going to save the women in the brothel.
In La Noire we get Jean Archer who can't seem to help but give information by mistake in the case appropriately titled "A Slip of the Tongue".
In RWBY, after an intense shouting match between Weiss and Blake, they have this exchange:
Weiss: You want to know why I despise the White Fang? It's because they're a bunch of liars, thieves, and murderers!
When Zii in Ménage à 3 breaks one of Gary's most prized Transformers and learns that it was a highly rare Overlord, she tries to pin it on a cleaning woman she made up: "Tragic, I know. Poor Overlord... never knew what hit him!" Gary than asks how did she know it was an Overlord.
In Kid Radd, Captain QB, after meeting with Crystal in a room they think is soundproof to discuss killing Radd, sees Sheena on the way out and asks if she heard any of it. Sheena responds that "like your friend said," the room is soundproof. Thankfully, since QB isn't too bright, he never suspects anything, enabling Sheena to leave without incident and help save Radd.
In General Protection Fault, after being shown the diary detailing her plans, Trudy launches into a rant about how Ki shouldn't have been able to find it, before stopping herself and asking if she had been "saying something incriminating." The damage has been done, though, and Nick no longer trusts her.
From The Simpsons: "I'm sorry, I can't divulge any information about that customer's secret, illegal account. [hangs up phone] Oh, crap, I shouldn't have said he was a customer. Oh, crap! I shouldn't have said it was a secret. Oh, crap! I certainly shouldn't have said it was illegal! Oh, it's too hot today."
From the episode "Wedding for Disaster":
Parson: I remember when she [Helen Lovejoy] used to be Helen Schartzbaum. Heck, I even remember when she was Harold Schartzbaum!
Another instance had our heroes being tried in juvenile court for egging Tom Anderson's house. Butt-Head tries to discredit Anderson's testimony by claiming that his vision wasn't strong enough to see exactly who threw the rotten eggs, pointing out that it could as easily have been Stewart Stevenson. The prosecutor then asks how Butt-Head could have known the eggs were rotten, unless he was the one that threw them. Oops.
In Batman Beyond, this is how Terry McGinnis almost immediately proves that Willie Watt is responsible for the strange occurrences at their high school.
In the Adventure Time episode "BMO Noire", Beemo is playing at being a hard-boiled private investigator while trying to find Finn's missing sock. At one point he asks Lorraine the chicken about the missing sock, and Lorraine "blabs" that she knows that it was Finn's sock that was stolen before BMO mentioned it.
OJ Simpson made this mistake while discussing his polygraph test with a reporter. When asked whether he had ever taken a polygraph test, Simpson replies with an emphatic "No." He then goes on to explain how he did go to the police station, did get hooked up to the machine, and watched the needles jump whenever his victims were mentioned.
Reporter: It sounds like you took a polygraph.
Simpson: YOU DON'T KNOW ABOUT POLYGRAPHS!'
Simpson then goes on to discuss in great detail how he took a polygraph, and why he doesn't believe it "counts" as a "real" polygraph.
A classic riddle has you as a detective trying to determine which of three people pistol-whipped a man to death. They all know the gun used is in custody. Inevitably, the one who did it is the one who says, "You don't think I beat him, did you?"
The next day the poor kid was brought onto The Today Show to be further questioned about this, and he got so nervous about getting his parents in trouble that he vomited.
A man in Florida vanished shortly after winning millions in the state lottery. The prime suspect was a woman whom he hired to manage his funds but was apparently embezzling them. After the man's body was found, she was again questioned by the police. Afterwards, she called a press conference and tearfully proclaimed her innocence, declaring that she "had been falsely accused of shooting another human being." However, the police had not revealed to anyone exactly how the man was killed.
The Japanese organization PRIDE FC used to sell DVDs of their fights months after they'd happened with English commentary dubbed in. The commentators would pretend to be watching the fights live. This came apart during an infamous incident in which the play-by-play man forgot what was going on and began telling his partner an amusing anecdote...about the fight they were calling. Written about here by Sean Baby (#4 in the list).
A similar incident happened on American Idol. While commenting on one of the performances, Paula Abdul accidentally gave her critique of a song which hasn't been performed yet, revealing that the judges sometimes write their critiques beforehand, based on the contestants' dress rehearsals.