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.
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.