Flowers for Your Grave - S1-E1
Continuity mistake: At the precinct checking Tisdale's alibi for the passport stamps, Castle asks why can't she just admit he was right. Ryan next to her is holding the receiver in a different way (look at the index finger) at the cut. (00:34:10)
Flowers for Your Grave - S1-E1
Continuity mistake: Beckett teases Castle after the visit to Harrison Tisdale, spelling out why he's obviously lying. During the scene, the passers-by change position between shots, especially noticeable at the beginning. (00:33:45)
Flowers for Your Grave - S1-E1
Continuity mistake: Harrison Tisdale hands Beckett his passport; it's facing opposite directions in the two shots. (00:33:25)
Flowers for Your Grave - S1-E1
Continuity mistake: Returning home after his arrest, Castle says "Just have to figure out why." Alexis in foreground puts a lock of hair behind her ear, but at the cut it's the same way it was before. (00:29:20)
Flowers for Your Grave - S1-E1
Continuity mistake: After she received the box with the book, Beckett puts it down on the desk, the lid just by the keyboard. It's then gone, and back there again. (00:25:40)
Flowers for Your Grave - S1-E1
Continuity mistake: James Patterson delivers the fun "Well, it's Castle we're talking about..." joke, one hand on top of the other. Next shot, and they are apart on the table. (00:23:30)
Flowers for Your Grave - S1-E1
Continuity mistake: During the poker game with the other authors, Stephen J. Cannell says "You're bluffing, Patterson." The way he holds the cards differs in the two shots. It happens again later after Patterson says that he wouldn't put a bullet in Alex Cross 's head. (00:22:40)
Flowers for Your Grave - S1-E1
Continuity mistake: "Prom queen" murder scene. Beckett' phone rings while Castle asks her about the motive. The janitor in the wide shot reached forward with his right arm, but when she answers, the guy's hand is on his hip. (00:18:50)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle repeats incredulous "A week?" when Beckett tells him how long it'll take for the print results to come out. The cop sitting by confirms nodding, and has both arms on the desk. Reverse angle, and the left arm is off the desk, and back to both as it goes back to the previous angle. (00:16:15)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle comes back from the police station at quarter to one AM with a cleaner shave than he had at the police station. (00:09:25)
Flowers for Your Grave - S1-E1
Continuity mistake: When Beckett shows Castle the picture of the flower-themed murder, in close-up the photo is laid out on an empty table, but it's on the pile of the other photos in the wider angle. (00:07:50)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle's mum is rather unapologetic about her leaking the compromising antics of her son in underwear, and talks to him patting him on the chest. She says "it's expected" and pulls her hands back, but they are still open in front of his chest in the next shot. (00:04:55)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle approaches his mother and daughter at the bar and orders "a hit of the bubbly." He kisses his daughter; there is one open notebook stacked on top of a closed red one. The angle changes and the open notebook shifted off the closed one. (00:04:35)
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.
Continuity mistake: When Beckett watches the weird/creepy video and a few images after seeing the ghost at the house, she hears a little girl laugh. However when Castle watched the video, that laugh happened at the moment with the ghost at the house, not after.
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.
Character mistake: Beckett identifies the area given for the Skype call as the whole city of Paris. It's hard to believe that Beckett knows the area of a foreign city by heart, the problem is also that she is wrong. Paris actually has an area of about 105 km² (41 sq mi).
Continuity mistake: When Castle comes home to Sophia waiting for him in his office, she is holding the Derrick Storm graphic novel; it keeps changing from open, to closed, even to her closing it every time we see it in her hands. It's very noticeable.
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.
