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: 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.
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?"