Trivia: Castle's Halloween costume is of Malcolm Reynolds, played by Nathan Fillion in the short-lived TV show "Firefly." Alexis asks him: "Didn't you wear that like five years ago?" Serenity, the film based on Firefly, was released 5 years before this episode aired.
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 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.
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)
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.
Answer: The networks are now having winter breaks. A mid season end of new episodes, when they come back after the new year, it picks up as if several months have gone by. Beckett suggested Valentine's Day as a "chick flick" to watch as she is moved in. Also some episodes are not scheduled to air in order.