Continuity mistake: When Beckett, Esposito and Ryan interview the fruit stand vendor, he states that he saw a bronze Mercedes drive by, to which Esposito replies, "That's Castle's car." In the previous scene at the car crash site, Ryan asks Esposito to check the back corner of the car for damage, which is silver or gray, not bronze, in color. (00:04:35)
Continuity mistake: When Beckett brings Castle to the campsite, he tells her he never would have set up camp near the ocean because of his research for Tropical Storm, and his irrational fear of tsunamis. Beckett then says to Castle, "You bought a beach house in the Hamptons." To which Castle replies, "Yeah, on the inland side, not the ocean side." But in 5x04 [Murder, He Wrote], Castle gives Beckett a tour of the Hamptons house, finishing out to the backyard with the sounds of waves crashing, and Castle saying, "This is actually my favorite part. The sound of the ocean, complete privacy..." (00:36:15 - 00:37:00)
Child's Play - S7-E4
Continuity mistake: When Castle is allowed to talk to Mrs. Ruiz's second graders, as he enters the classroom, he is hit in the temple with an object thrown at him and holds his hand to his head in pain. After he turns to say something to Beckett, as he turns back, not only has the hand on his head switched, it's also much lower, down on his chin. (00:07:55)
I, Witness - S7-E13
Continuity mistake: In the morning after the murder, at their loft Beckett and Castle are talking about the case. The hood on Kate's grey jumper either completely covers her left shoulder, or not, depending from shot to shot. (00:14:35)
I, Witness - S7-E13
Continuity mistake: When Castle and Beckett are in bed, their pillow cases are dark and patterned. When Beckett wakes up to find Castle gone, the pillow cases are white. (00:30:00 - 00:30:40)
I, Witness - S7-E13
Continuity mistake: Beckett has just walked into the P.I. office with two coffees to meet Castle. The way she holds the coffee in her right hand changes instantly. At first, she's holding the top of the cup, then she's holding it on the bottom. (00:31:15)
Continuity mistake: When Castle and the flight attendants are attempting to obtain fingerprints from a suspect, the liquid in the cup that he throws away changes colors. (00:16:25)
Continuity mistake: Alexis' necklace changes in almost every single shot that it's shown. Sometimes it's a single loop; sometimes it's two; sometimes it's three; sometimes the shade of red is darker or lighter; sometimes the loops are big or small and so on. It's very noticeable.
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.