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.
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.