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.
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?
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.
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.
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.
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 episode 2-5, "When the Bough Breaks," when Rick is talking to his mother regarding handing out her pamphlets at his book signing party, he opens his beer and throws the cap on the counter, when the shot changes you see him opening the beer again.