Plot hole: On the recording that Captain Montgomery left for Beckett, the conversation is exclusively between Montgomery and Bracken. But as established in "Knockout", Montgomery was only a rookie during the Bob Armen incident; as two veterans who are more than capable of speaking up for themselves, it seems unlikely that Raglan and McCallister would choose a newbie as their voice, particularly to the assistant D.A who's blackmailing them.
Suggested correction: Maybe they thought that fewer things could go wrong with an "expert" of some sorts. Rookies tend to learn along the way, and do anything possible when starting out.
Continuity mistake: In the flashback of Beckett and Montgomery, when Montgomery finds her in the archive room studying her mother's murder case, Beckett says that she was unable to find any leads worth following. But in season three, when Montgomery explains to Castle that that encounter was when he first met Kate, he says "she found some things that didn't add up", suggesting that she did find a clue worth investigating.
Continuity mistake: At the end of the episode, the Mercedes S class that is burning is not the same car that Castle drove previously in the episode, it's an older model one. Either it's a mistake or has to do something with the plot resolution, decide yourselves...
Continuity mistake: When Beckett, Esposito and Ryan interview the fruit stand vendor, he states that he saw a bronze Mercedes drive by, to which Esposito replies, "That's Castle's car." In the previous scene at the car crash site, Ryan asks Esposito to check the back corner of the car for damage, which is silver or gray, not bronze, in color. (00:04:35)
Continuity mistake: When Beckett brings Castle to the campsite, he tells her he never would have set up camp near the ocean because of his research for Tropical Storm, and his irrational fear of tsunamis. Beckett then says to Castle, "You bought a beach house in the Hamptons." To which Castle replies, "Yeah, on the inland side, not the ocean side." But in 5x04 [Murder, He Wrote], Castle gives Beckett a tour of the Hamptons house, finishing out to the backyard with the sounds of waves crashing, and Castle saying, "This is actually my favorite part. The sound of the ocean, complete privacy..." (00:36:15 - 00:37:00)
Child's Play - S7-E4
Continuity mistake: When Castle is allowed to talk to Mrs. Ruiz's second graders, as he enters the classroom, he is hit in the temple with an object thrown at him and holds his hand to his head in pain. After he turns to say something to Beckett, as he turns back, not only has the hand on his head switched, it's also much lower, down on his chin. (00:07:55)
I, Witness - S7-E13
Continuity mistake: In the morning after the murder, at their loft Beckett and Castle are talking about the case. The hood on Kate's grey jumper either completely covers her left shoulder, or not, depending from shot to shot. (00:14:35)
I, Witness - S7-E13
Continuity mistake: When Castle and Beckett are in bed, their pillow cases are dark and patterned. When Beckett wakes up to find Castle gone, the pillow cases are white. (00:30:00 - 00:30:40)
I, Witness - S7-E13
Continuity mistake: Beckett has just walked into the P.I. office with two coffees to meet Castle. The way she holds the coffee in her right hand changes instantly. At first, she's holding the top of the cup, then she's holding it on the bottom. (00:31:15)
I, Witness - S7-E13
Revealing mistake: When Castle answers his phone at the start of the episode, his phone is on the lock screen instead of in call mode.
Revealing mistake: When Detective Ryan calls Captain Gates after apprehending Jerry Tyson at Michael Boudreaux's apartment, Ryan's phone is not in call mode.
Continuity mistake: When Castle and the flight attendants are attempting to obtain fingerprints from a suspect, the liquid in the cup that he throws away changes colors. (00:16:25)
Continuity mistake: Alexis' necklace changes in almost every single shot that it's shown. Sometimes it's a single loop; sometimes it's two; sometimes it's three; sometimes the shade of red is darker or lighter; sometimes the loops are big or small and so on. It's very noticeable.
Revealing mistake: At the beginning when the murder victim falls through the ceiling of the elevator, there is a bag of blood that show right behind his head.
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.
Audio problem: When Martha arrives at the beginning of the episode, she says to Castle, "I didn't want to disturb you in case you wanted to sleep in." But her lips don't move when she says "sleep in."
Continuity mistake: When Castle gives Beckett a mug of coffee at the beginning of the episode, she isn't holding it by the handle, but in the shot immediately afterwards she is.
Death Wish - S8-E17
Continuity mistake: Beckett keeps a jar of nuts on her desk. When she's talking to Castle about Lars, she reaches over her desk to put the jar down. But in the following shot when Castle stands up, both her hands are suddenly in front of her laptop, clasped together.
Death Wish - S8-E17
Continuity mistake: When Castle beings theorising that Genevieve might be a genie and that she wants him to be her new master, Beckett is holding a glass in both hands. In the following shot, she's holding it with just one hand.