Audio problem: When Martha arrives at the beginning of the episode, she says to Castle, "I didn't want to disturb you in case you wanted to sleep in." But her lips don't move when she says "sleep in."
Continuity mistake: When Castle gives Beckett a mug of coffee at the beginning of the episode, she isn't holding it by the handle, but in the shot immediately afterwards she is.
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.