Close Encounters of the Murderous Kind - S3-E9
Trivia: In this episode, Castle says the words "My partner is crazy and may start firing at any moment" in Chinese. Beckett then asks him "Semester abroad?", to which he replies "Nah, a TV show I used to love". This is a reference to Firefly, a TV show starring Nathan Fillion in which characters occasionally spoke in Chinese.
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.