Factual error: On the way to the Hamptons, Castle's car is driving on the left side of the road, even though they're in the US (where people drive on the right side of the road). (00:03:10)
Revealing mistake: After Castle and Beckett are arrested for interfering in Chief Brady's investigation, a deputy tells them that Brady wants to speak to them; Beckett stands up to leave the holding cell, but is held back by the pair of handcuffs chaining her to the bench. The cuff is not actually on Stana Katic's wrist; she's just holding it in her hand.
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.