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 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: 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.
Continuity mistake: When Kyra introduces Greg to Castle, Greg takes Kyra away to greet the new arriving guests. He places his left hand on her right shoulder twice between shots.
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.
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)
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)
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.
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.
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.
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.
Continuity mistake: In the opening scene, when the rider is knocked off his bike by the car, the bike ends up under the front wheel of the car. When the perpetrator drives off, the bike is some distance away from the car.
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.