Cloudy with a Chance of Murder - S5-E2
Continuity mistake: When Beckett is trying to get dressed for work at the beginning, she takes off a blouse she deems unsuitable and the bullet scar on her chest, which is usually at the start of her cleavage line, is missing. (00:00:25)
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)
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)
Continuity mistake: Castle gives Beckett a coffee mug in a very loving way by moving her hand to hold the mug by the handle while she is reading a file and not looking. Then in the very next scene she is holding the mug on the bottom in her palm. (00:05:24)
Continuity mistake: When they first arrest Penelope they show her first fingernail broken. In the next scene when she's talking about the nail, she shows her middle fingernail broken.
Continuity mistake: When Beckett watches the weird/creepy video and a few images after seeing the ghost at the house, she hears a little girl laugh. However when Castle watched the video, that laugh happened at the moment with the ghost at the house, not after.
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)
The Fast and the Furriest - S5-E20
Continuity mistake: Beckett's sweatshirt changes position on her left shoulder throughout the scene in which she and Castle are sitting in bed discussing Bigfoot. Her sweatshirt is initially covering her shoulder and then keeps going lower and lower off her shoulder every time the camera comes back to her .
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.