Home Is Where the Heart Stops - S1-E7
Visible crew/equipment: When Castle and Beckett step into the elevator whilst talking about The New York Review of Books, a cameraman is reflected in the left door of the elevator as it closes and the scene ends.
Home Is Where the Heart Stops - S1-E7
Continuity mistake: After the two talked to the victim's daughter, Castle buys Beckett a soda. The way he holds the can as he hands the soda to her changes between consecutive shots.
Home Is Where the Heart Stops - S1-E7
Continuity mistake: When Esposito pulls up Evan Mitchell's rap sheet, it says he is 5'9", but in Mitchell's mugshot, the top of his head crosses the 6' mark.
Home Is Where the Heart Stops - S1-E7
Factual error: The shots of the West Side towards the end of the episode are reversed: you can see traffic on the West Side Highway moving in the wrong directions. (00:40:10)
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.