Factual error: When Castle and Beckett go to talk to the victim's assistant, there is a chalk outline on the floor where the body was discovered. Although it's common in police dramas, chalk outlines are not actually police procedure, because it contaminates the crime scene. (00:08:40)
Continuity mistake: When Castle and Beckett go to question Jeffrey McGuigan, Beckett raises her badge twice: once while the camera is on Guy Wilson, and a second time when the shot cuts and the camera is on Stana Katic. (00:25:15)
To Love and Die in L.A. - S3-E22
Visible crew/equipment: At the pool, after Beckett makes a stunning entrance from the water, a white reflector screen is seen on Ganz's sunglasses. (00:31:40)
Continuity mistake: When Ryan crosses out the name "I. Seperich" on the "Dirty Dozen" list, the thickness of the line changes between shots, as he talks to Castle.
Revealing mistake: When Castle arrives at the murder scene and views the victim's body, the "corpse's" eyelids are twitching.
Visible crew/equipment: When Castle pokes his head through the doorway with his eyes closed before walking in on Alexis again, in the shot facing Alexis the boom mic hovers in front of her, at the bottom of the screen. (00:40:50)
Continuity mistake: The guy at the door says "I purchased a ton of crap at that place" and the door is partially open next to him. It cuts to a barely different angle as he says "come on in" and the door is instantly wide open. (00:25:25)
Character mistake: They find the DeLorean and the licence plate is shown: LFM-26W1. Esposito calls in and says the car needs towing: "'81-'82 DeLorean, New York plates, JLD..." Nothing like the actual licence plate.
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.