Nanny McDead - S1-E2
Continuity mistake: At the loft, Alexis is putting away the leftovers and clearing the kitchen. Her hair moves back and forth over her right shoulder throughout the scene. (00:10:30)
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: 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)
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.
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: 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)
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)
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)
Nanny McDead - S1-E2
Continuity mistake: After talking to Alexis at the end of the episode, Castle closes his laptop and puts it on the desk. He looks for the picture frame, and in the background you can see in two shots that the laptop is open. Wider angle, it's closed again. (00:40:15)
Nanny McDead - S1-E2
Continuity mistake: Castle and Beckett are walking with Mr. Peterson asking him about the possible affair. He says that she was making "Us" dinner; there's a woman in the background, grey coat and a scarf. The scarf changes position at the cut when they call him out on the pronoun. (00:20:25)
Nanny McDead - S1-E2
Continuity mistake: Interviewing Chloe, the protagonists tell her that Sara's ex thought she had a new guy. Look at the cyclist in the background (that already made an appearance earlier); he reappears in the next shot as she goes "Uhm...", and he moved backwards. (00:18:15)
Nanny McDead - S1-E2
Continuity mistake: When Castle makes the joke about Kate being both controlling and disapproving, his elbow is on the right, then on the left of the railing bar. (00:16:50)
Nanny McDead - S1-E2
Continuity mistake: Castle is on a break at home. Alexis asks him "Who got killed today?" He's putting the cap on a spice dispenser, empty. When she follows with "Do they know who did it?" the dispenser refilled. He then puts it down, but it's back in his hands at the cut. (00:09:10)
Nanny McDead - S1-E2
Continuity mistake: When Beckett takes the call at the beginning of the episode, her fingers change position on the phone between shots. (00:00:50)
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)
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.