Continuity mistake: When Ryan crosses out the name "I. Seperich" on the "Dirty Dozen" list, the thickness of the line changes between shots, as he talks to Castle.
Continuity mistake: When Castle and Beckett go to question Jeffrey McGuigan, Beckett raises her badge twice: once while the camera is on Guy Wilson, and a second time when the shot cuts and the camera is on Stana Katic. (00:25:15)
Continuity mistake: The guy at the door says "I purchased a ton of crap at that place" and the door is partially open next to him. It cuts to a barely different angle as he says "come on in" and the door is instantly wide open. (00:25:25)
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.