Plot hole: When Ryan asks Beckett where Castle is, Beckett says something like "I don't know. I thought that the death of a bridesmaid would be right up his alley." and Ryan replies "Probably heard the word "wedding" and got cold feet." Only problem is, how could Castle have known that? He was duct-taped to a chair at the time Beckett called and couldn't answer the phone. We see Beckett right after he falls on the table and we don't see her leaving a voice mail or send a text message so he couldn't have known, especially since he asked "So, bridesmaid huh?"
Plot hole: The security camera images of Castle kissing Kyra on the roof are completely inexplicable. The angle at which the images are taken are near enough identical to the angles at which the rooftop scene were shot. There were no pillars, poles or high walls for a security camera to be attached to at those particular angles, and certainly nowhere a photographer could hide, so where did the images come from?
Suggested correction: Beckett had Kyra followed, because she was a suspect. The photos were taken by the person following her.
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.
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 Beckett and Castle are talking about the failed sting on Rathborne, Beckett's hand jumps back and forth from gripping her coffee mug by the handle in the close ups to the bottom in the wide shots. (00:36:45)
Continuity mistake: When the Captain hands Beckett his flask, from behind she unscrews the cap and lifts it to her mouth. We then cut to a front-on shot of Beckett and she lifts it to her mouth a second time.
Continuity mistake: When Castle asks Trucho how he burned his hand, Trucho places the ice pack to his eye twice between shots.
Revealing mistake: When Kate gets the info that the killer is the same one who killed her mother, the back of her shirt is shown twice, revealing each time that it is fixed with needles to fit perfectly.
Continuity mistake: After Special Agent Shaw tells Beckett to go home when they believe a murder took place in a multi-story car park, Beckett touches her hair with her right hand. She is wearing gloves on both of her hands when she does this. In the shot immediately afterwards however, her right hand is bare and she is holding the glove in her left hand.
Factual error: The con is said to be electrocuted. But the jump start cables are connected to handcuffs which would short the electrical circuit and most probably melt the handcuff chain, but wouldn't electrocute the victim. (00:02:50)
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.
Audio problem: When Demming writes "Stolen books" on the white board and says, "Killed for a fortune in stolen books, so I'll run the work crews and see if anybody has priors", his lips don't match what he's saying at all.
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.
Visible crew/equipment: When Castle pokes his head through the doorway with his eyes closed before walking in on Alexis again, in the shot facing Alexis the boom mic hovers in front of her, at the bottom of the screen. (00:40:50)
Character mistake: They find the DeLorean and the licence plate is shown: LFM-26W1. Esposito calls in and says the car needs towing: "'81-'82 DeLorean, New York plates, JLD..." Nothing like the actual licence plate.
Continuity mistake: When Castle and Beckett go to question Jeffrey McGuigan, Beckett raises her badge twice: once while the camera is on Guy Wilson, and a second time when the shot cuts and the camera is on Stana Katic. (00:25:15)
Continuity mistake: The guy at the door says "I purchased a ton of crap at that place" and the door is partially open next to him. It cuts to a barely different angle as he says "come on in" and the door is instantly wide open. (00:25:25)
Factual error: When Castle and Beckett go to talk to the victim's assistant, there is a chalk outline on the floor where the body was discovered. Although it's common in police dramas, chalk outlines are not actually police procedure, because it contaminates the crime scene. (00:08:40)
