Continuity mistake: The precinct number (12th) is not firmly established until Episode 6 of Season 1 when we see that number painted on the elevator doors at 28:28. Prior to that (Episodes 1, 3, 4 and 5), shots of the outside of the building, including squad car markings, indicate it's the 9th Precinct. The first hint that it might be the 12th is in Episode 4 (01:20) when we see 12th Precinct collar brass on the uniformed officer. But we still see the 9th Precinct building and cars used through to Season 3: 1-1 (06:33); 1-1 (21:03); 1-3 (30:42); 1-4 (11:06); 1-5 (20:44); 1-10 (17:30); 2-3 (24:40); 2-8 (03:50); 2-9 (04:23); 2-15 (28:46); 2-18 (39:17); 2-19 (30:55); 2-20 (19:47); 2-21 (07:01); 2-22 (36:41); 2-23 (5:38); 2-23 (15:15); 2-24 (27:290; 3-1 (25:58); 3-7 (08:53). The first time we see a squad car marked "12th PCT" is 2-22 (02:19), and the first time we see a building marked "12" is 3-13 (33:39).
Flowers for Your Grave - S1-E1
Continuity mistake: When Castle finishes talking to Gina about his new book that's due, he raises his champagne flute with his right hand, but when he actually imbibes the alcohol, the flute is in his left hand. (00:04:25)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle approaches his mother and daughter at the bar and orders "a hit of the bubbly." He kisses his daughter; there is one open notebook stacked on top of a closed red one. The angle changes and the open notebook shifted off the closed one. (00:04:35)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle's mum is rather unapologetic about her leaking the compromising antics of her son in underwear, and talks to him patting him on the chest. She says "it's expected" and pulls her hands back, but they are still open in front of his chest in the next shot. (00:04:55)
Flowers for Your Grave - S1-E1
Continuity mistake: Just before Beckett walks up to Castle, he is talking to Alexis. Alexis' hair keeps moving back and forth over her left shoulder throughout the scene. (00:06:05)
Flowers for Your Grave - S1-E1
Continuity mistake: Kate Beckett has just walked up to Castle and told him that the police would like to question him about a murder. The way she holds her badge is different throughout the scene. Note the position of her thumb. (00:06:20)
Flowers for Your Grave - S1-E1
Continuity mistake: When Beckett shows Castle the picture of the flower-themed murder, in close-up the photo is laid out on an empty table, but it's on the pile of the other photos in the wider angle. (00:07:50)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle comes back from the police station at quarter to one AM with a cleaner shave than he had at the police station. (00:09:25)
Flowers for Your Grave - S1-E1
Continuity mistake: Alexis is trying to get her father to tell her how the interview with the police went as Castle playfully pushes her along the corridor. Castle is holding the bottle of whipped cream in his right hand with the bottle positioned above his daughter's elbow. Cut to the immediate next shot and the bottle is now underneath Alexis' elbow. (00:10:20)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle repeats incredulous "A week?" when Beckett tells him how long it'll take for the print results to come out. The cop sitting by confirms nodding, and has both arms on the desk. Reverse angle, and the left arm is off the desk, and back to both as it goes back to the previous angle. (00:16:15)
Flowers for Your Grave - S1-E1
Continuity mistake: "Prom queen" murder scene. Beckett' phone rings while Castle asks her about the motive. The janitor in the wide shot reached forward with his right arm, but when she answers, the guy's hand is on his hip. (00:18:50)
Flowers for Your Grave - S1-E1
Continuity mistake: During the poker game with the other authors, Stephen J. Cannell says "You're bluffing, Patterson." The way he holds the cards differs in the two shots. It happens again later after Patterson says that he wouldn't put a bullet in Alex Cross 's head. (00:22:40)
Flowers for Your Grave - S1-E1
Continuity mistake: James Patterson delivers the fun "Well, it's Castle we're talking about..." joke, one hand on top of the other. Next shot, and they are apart on the table. (00:23:30)
Flowers for Your Grave - S1-E1
Continuity mistake: After she received the box with the book, Beckett puts it down on the desk, the lid just by the keyboard. It's then gone, and back there again. (00:25:40)
Flowers for Your Grave - S1-E1
Continuity mistake: When the cops tear down the board with the serial killer case, you can see already next to the lawyer the note in grey ink that says that the object used to suffocate him was wrong, which is a conclusion Bishop comes to later in the case resolution, with the notes on the other two victims in the same ink. (00:28:40)
Flowers for Your Grave - S1-E1
Continuity mistake: Returning home after his arrest, Castle says "Just have to figure out why." Alexis in foreground puts a lock of hair behind her ear, but at the cut it's the same way it was before. (00:29:20)
Flowers for Your Grave - S1-E1
Continuity mistake: Harrison Tisdale hands Beckett his passport; it's facing opposite directions in the two shots. (00:33:25)
Flowers for Your Grave - S1-E1
Continuity mistake: Beckett teases Castle after the visit to Harrison Tisdale, spelling out why he's obviously lying. During the scene, the passers-by change position between shots, especially noticeable at the beginning. (00:33:45)
Flowers for Your Grave - S1-E1
Continuity mistake: At the precinct checking Tisdale's alibi for the passport stamps, Castle asks why can't she just admit he was right. Ryan next to her is holding the receiver in a different way (look at the index finger) at the cut. (00:34:10)
Flowers for Your Grave - S1-E1
Continuity mistake: Castle and Judge Markway are talking about the golf course. In the close-up on Beckett, the same couple walks again by the doors in the background like in the previous shot. (00:35:30)
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.