Continuity mistake: Jennifer Beals' blouse mysteriously changes from white to blue while they are in the CIA secret bunker prior to heading out for the final confrontation.
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)
Continuity mistake: When Beckett and Castle are talking about the failed sting on Rathborne, Beckett's hand jumps back and forth from gripping her coffee mug by the handle in the close ups to the bottom in the wide shots. (00:36:45)
Continuity mistake: When Castle gets back from helping Alexis with her friend and thanks Beckett for taking care of Fagan (Alexis' egg), just after her line, "Yeah well, he was easy. He didn't even fuss when I put him to bed", Ryan and Esposito come in and Ryan is holding a missing persons poster of Elizabeth McGinty. As soon as they walk in, Ryan is holding the poster with the front facing the camera. But two shots later he is holding it with the back facing the camera.
Fool Me Once - S2-E4
Continuity mistake: Castle and Beckett corner the con woman in her car and she flashes her badge. The way she holds it differs between shots from outside the car and inside the car.
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.
Fool Me Once - S2-E4
Continuity mistake: When Beckett goes to the bathroom to read Castle's book and Castle peers over the top of the cubical to tell her what page the sex scene is on, she is holding the book with her fingers between the pages dividing the book into 2 sections. These 2 sections switch to 3 and then back to 2 between shots.
Continuity mistake: When Beckett, Castle and Capt. Montgomery are walking through the precinct, after Castle and Beckett checked on Alexis as she had been categorizing personal belongings, and Castle is talking about how he watched Alexis from the bushes the first day of preschool; Montgomery states he followed his son's bus all the way to the Adirondacks. In the final episode of season 3, Montgomery had his two daughters, and wife at his funeral. There was no son.
Continuity mistake: When Castle is freezing stuff in his apartment and Martha starts talking to Alexis about her forthcoming exam, she is either holding an iPod or a glass of wine in her right hand between shots.
Continuity mistake: When Castle asks Trucho how he burned his hand, Trucho places the ice pack to his eye twice between shots.
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: 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)
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)
Continuity mistake: Castle gives Beckett a coffee mug in a very loving way by moving her hand to hold the mug by the handle while she is reading a file and not looking. Then in the very next scene she is holding the mug on the bottom in her palm. (00:05:24)
Nanny McDead - S1-E2
Continuity mistake: Esposito suggests going pick Chloe up. Castle interjects, and Beckett turns towards him; she was leaning against the doorframe but removed the hand, which is back on the frame in the next shot. (00:30:55)
Nanny McDead - S1-E2
Continuity mistake: When the sleazy husband says "We had sex, okay?" he is wearing a ring on the middle finger of his right hand. When he answers Castle's question the ring moves to the fourth finger. (00:29:45)
Nanny McDead - S1-E2
Continuity mistake: When Castle's mom says she's 1/4 responsible for Alexis' genes, the glass in front of her has merely a few drops left in it. When Castle leaves and she calls him "flatfoot", the glass is still mostly empty but there's about twice as much wine left. (00:10:30)
Nanny McDead - S1-E2
Continuity mistake: When Alexis punctuates her Grandma's statement saying "you were the crazy homeless woman", she is holding the big wooden spoon up, but it's down against the rim of the bowl in the next shot. (00:09:35)
Flowers for Your Grave - S1-E1
Continuity mistake: When Judge Markway signs the warrant on Castle's back, the paper changes position between shots, and there's a white sheet between the board and Castle's back that is folded in the wider angles but sticks out straight in the close-up. (00:36:20)
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.