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...
Plot hole: All three murder suspects claim to have seen a picture above the fridge of the hotel room. This picture however is only in the hotel room where the actual murder happened, not in the room that is shown in the video, so they couldn't have seen it.
Under Fire - S6-E11
Other mistake: At some point during filming, Stana Katic injured her right hand. At episode's end, when Beckett hugs Esposito and Ryan after they're rescued, her index and middle fingers are taped together, and the injury doesn't appear in any other scene. (00:41:00)
Smells Like Teen Spirit - S6-E15
Factual error: German bearer bonds would never have English writing on them, and furthermore instead of just saying "German bearer bonds" the company or other entity that issued them would be named.
In the Belly of the Beast - S6-E17
Continuity mistake: After Beckett gets back from her assassination assignment, she washes up in a bathroom and places the gun she was given in her front waistband near her stomach. Then she goes to meet Lazarus (Vulcan Simmons) in the basement, who realizes she's Beckett. When she pulls out the gun, she reaches behind her back to get it. (00:27:25 - 00:31:00)
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.
Audio problem: Ryan yells "show me those hands" but the audio happens before we actually see him move his lips, meaning it is terribly out of sync.
Plot hole: Beckett is framed for the murder of Vulcan Simmons by someone (likely connected to Senator Bracken) who has access to her backup weapon locked in a safe in her apartment. It's never really proven that she's innocent; the murder weapon is never recovered, and the real murderer is never brought to justice. And though she's still technically a murder suspect, Beckett is allowed - after finding the evidence for which she's been searching - to act in her law enforcement capacity and arrest Senator Bracken.
Suggested correction: She had evidence, (the tape) that he was a murderer and probably explained before the arrest. That should be enough to prove her innocence, and to also prove him guilty.
The tape is proof of Bracken's guilt, not of Beckett's innocence. And as we've seen, Bracken is too careful to get caught; he wouldn't clear her name just to help her, or without something in it for himself. People would start asking questions why, and the truth of his criminal wrongdoings would be exposed. And though it was later retconned in S8 that Mr. Smith helped clear her, it took two years for the writers to address it, so as a standalone episode, it's still a gaping hole in the story.
With proof on Bracken, that could also prove Beckett's innocence. It's two birds with one stone. Nobody believed her anyway and she was accused of murder, but once the news on Bracken gets out, nobody has any reason not to take her more seriously.
Continuity mistake: At the end, Beckett spills coffee on the letter. In the first shot, before she frantically blots the spilled coffee, it says that the writer is "a junior at P.S. 370." Afterwards, this has changed to "P.S. 311." (00:40:40)
Like Father, Like Daughter - S6-E7
Continuity mistake: When Castle and Alexis visit Frank at the prison in Pennsylvania, as he's brought in, the guard removes his handcuffs. In one shot, Frank's arms are flat on the table, and in the following shot, his left arm is raised. (00:08:20)
Continuity mistake: When Kate gets a call from Lanie who asks her to come down to the morgue, Kate's jacket is beige. When Kate enters the morgue, it's black/dark blue. (00:07:40)
The Good, the Bad & the Baby - S6-E10
Continuity mistake: When Lanie arrives at the precinct to check on the baby, her shirt is tucked into her jeans, as seen when she bends over to pick the baby up. When the shot changes to behind Lanie, her shirt is untucked, and then when the shot changes to the front of Lanie, her shirt is tucked in again.
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.
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.
