Continuity mistake: When Beckett and Castle kiss at his party at the end of the episode, the camera is behind Castle, and Beckett's head is leaning toward her left shoulder. When the shot switches to behind Beckett, her head is leaning to the right. Then it switches back to left. (00:38:05)
Continuity mistake: Castle and Beckett are talking about the case in the precinct and his coffee runs out. Beckett offers to go refill the mug. She grabs his white mug in her right hand. In the next shot, it is now in her left hand. A blue mug is in her right hand instead. (00:05:15)
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)
Trivia: When Ryan and Esposito are searching for Jones the bodyguard, the man they first approach is Kris Brkljac, to whom Stana Katic has been married since 2015. (00:05:35)
Cloudy with a Chance of Murder - S5-E2
Continuity mistake: When Beckett, Ryan, and Esposito are discussing Castle's date with Kristina Cottera, Beckett's fork is full of food in a long shot, which disappears in the following close-up without her eating anything. (00:32:15)
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.