Deliberate mistake: When Ryan and Esposito give Beckett the surveillance tape of Sophie and Uncle Teddy, Beckett's computer reads the disc and plays the tape incredibly fast. Faster than any desktop PC I've ever seen.
Continuity mistake: When Castle gets back from helping Alexis with her friend and thanks Beckett for taking care of Fagan (Alexis' egg), just after her line, "Yeah well, he was easy. He didn't even fuss when I put him to bed", Ryan and Esposito come in and Ryan is holding a missing persons poster of Elizabeth McGinty. As soon as they walk in, Ryan is holding the poster with the front facing the camera. But two shots later he is holding it with the back facing the camera.
Fool Me Once - S2-E4
Continuity mistake: Castle and Beckett corner the con woman in her car and she flashes her badge. The way she holds it differs between shots from outside the car and inside the car.
Character mistake: In the scene where Castle and Kate are being told that the victim's SIM card is broken and the last two digits of the phone number are missing, Castle says that they have 99 possibilities, which mathematically is wrong. Obviously the writer didn't count the combination 00. The correct number of possibilities is 100. (00:08:40)
Continuity mistake: When Ryan crosses out the name "I. Seperich" on the "Dirty Dozen" list, the thickness of the line changes between shots, as he talks to Castle.
Fool Me Once - S2-E4
Continuity mistake: When Beckett goes to the bathroom to read Castle's book and Castle peers over the top of the cubical to tell her what page the sex scene is on, she is holding the book with her fingers between the pages dividing the book into 2 sections. These 2 sections switch to 3 and then back to 2 between shots.
Character mistake: Castle claims that they are technically standing on Russian soil inside the consulate. Contrary to popular belief foreign diplomatic missions, while being afforded special privileges (ie. Diplomatic immunity), are not considered sovereign territory of the represented state. Because of that Castle and Beckett are in fact on U.S. soil.
Character mistake: When Beckett is bemoaning losing her job with the government, she says she hasn't been out of work since she was fifteen. But in "Always" at the end of season four, she is suspended by Captain Gates and chooses instead to resign from the force.
Character mistake: The killer's motive for the murder is getting kicked out of the band akin to Beatles drummer Pete Best, and Castle whispers to the camera that bass player Stu Sutcliffe would have been a more appropriate comparison. Sutcliffe quietly quit the Beatles voluntarily, while Best was fired, with his dismissal becoming widely-known public knowledge, so the comparison to Best actually is more applicable.
Continuity mistake: When Beckett, Castle and Capt. Montgomery are walking through the precinct, after Castle and Beckett checked on Alexis as she had been categorizing personal belongings, and Castle is talking about how he watched Alexis from the bushes the first day of preschool; Montgomery states he followed his son's bus all the way to the Adirondacks. In the final episode of season 3, Montgomery had his two daughters, and wife at his funeral. There was no son.
Factual error: The team is discussing the location of the Widmark hotel which the detective says is downtown. Beckett then looks at the map and locates it only 5 blocks from E 72nd street, which is UPTOWN in NYC. Furthermore the map shows E 72 intersecting Broadway which is on the west side of Manhattan. This entire mapping exercise is incorrect.
Continuity mistake: When Castle is freezing stuff in his apartment and Martha starts talking to Alexis about her forthcoming exam, she is either holding an iPod or a glass of wine in her right hand between shots.
Continuity mistake: When Castle asks Trucho how he burned his hand, Trucho places the ice pack to his eye twice between shots.
Continuity mistake: The precinct number (12th) is not firmly established until Episode 6 of Season 1 when we see that number painted on the elevator doors at 28:28. Prior to that (Episodes 1, 3, 4 and 5), shots of the outside of the building, including squad car markings, indicate it's the 9th Precinct. The first hint that it might be the 12th is in Episode 4 (01:20) when we see 12th Precinct collar brass on the uniformed officer. But we still see the 9th Precinct building and cars used through to Season 3: 1-1 (06:33); 1-1 (21:03); 1-3 (30:42); 1-4 (11:06); 1-5 (20:44); 1-10 (17:30); 2-3 (24:40); 2-8 (03:50); 2-9 (04:23); 2-15 (28:46); 2-18 (39:17); 2-19 (30:55); 2-20 (19:47); 2-21 (07:01); 2-22 (36:41); 2-23 (5:38); 2-23 (15:15); 2-24 (27:290; 3-1 (25:58); 3-7 (08:53). The first time we see a squad car marked "12th PCT" is 2-22 (02:19), and the first time we see a building marked "12" is 3-13 (33:39).
Flowers for Your Grave - S1-E1
Continuity mistake: Just before Beckett walks up to Castle, he is talking to Alexis. Alexis' hair keeps moving back and forth over her left shoulder throughout the scene. (00:06:05)
Plot hole: Brandt sabotages the mercenaries' explosives so they are killed when trying to escape. No real team of professionals would let the rich yahoo who hired them touch their gear. Nor would they use any explosives he provided without (at the bare minimum) inspecting them first. It's a plot hammer to wrap up what happened to the mercs so they can move on to Brandt's capture.
Suggested correction: So, they knew they would be framed/killed at the end? Also, if he was paying or threatening them, then why wouldn't they listen to him?
Walk up to a professional you have hired and is doing his job. Plumber, AC tech, whatever. Ask him if you can mess around with his stuff while he's working. What do you think he'll say? Especially if your messing with it could cause harm to him.
Audio problem: When Beckett is talking to Matthew's family about his "personal ghost," as his sister put it. About half-way through her line, "I showed some of Matthew's drawings to one of our therapists and he said it looked like he might have witnessed something disturbing, seen something very violent", there is a shot from behind Beckett facing Matthew's parents. In this shot, Beckett's lips don't match what she is saying.
Revealing mistake: When Castle arrives at the murder scene and views the victim's body, the "corpse's" eyelids are twitching.
Other mistake: Beckett points out to the murderous security guard that some graffiti magically appears on the tape, showing the live image was replaced with older pre-recorded footage. "Do you see that? It's actually kinda hard to spot." Except the graffiti doesn't appear at the point where the live feed restarts (when the guard enters the shot), it only appears on the footage after a cut away and then back.
