Continuity mistake: At the end of the episode, the Mercedes S class that is burning is not the same car that Castle drove previously in the episode, it's an older model one. Either it's a mistake or has to do something with the plot resolution, decide yourselves...
Continuity mistake: When they first arrest Penelope they show her first fingernail broken. In the next scene when she's talking about the nail, she shows her middle fingernail broken.
Continuity mistake: When the Captain hands Beckett his flask, from behind she unscrews the cap and lifts it to her mouth. We then cut to a front-on shot of Beckett and she lifts it to her mouth a second time.
Continuity mistake: When Beckett and Castle kiss at his party at the end of the episode, the camera is behind Castle, and Beckett's head is leaning toward her left shoulder. When the shot switches to behind Beckett, her head is leaning to the right. Then it switches back to left. (00:38:05)
Headhunters - S4-E21
Continuity mistake: During Shea's interrogation scene, he has blood running from his head down to his eyebrow which collects into a blob. Between shots, this blob of blood disappears and reappears.
The Fast and the Furriest - S5-E20
Continuity mistake: Beckett's sweatshirt changes position on her left shoulder throughout the scene in which she and Castle are sitting in bed discussing Bigfoot. Her sweatshirt is initially covering her shoulder and then keeps going lower and lower off her shoulder every time the camera comes back to her .
Continuity mistake: After Special Agent Shaw tells Beckett to go home when they believe a murder took place in a multi-story car park, Beckett touches her hair with her right hand. She is wearing gloves on both of her hands when she does this. In the shot immediately afterwards however, her right hand is bare and she is holding the glove in her left hand.
Continuity mistake: When Kyra introduces Greg to Castle, Greg takes Kyra away to greet the new arriving guests. He places his left hand on her right shoulder twice between shots.
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)
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)
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)
Continuity mistake: Castle and Beckett are talking about the case in the precinct and his coffee runs out. Beckett offers to go refill the mug. She grabs his white mug in her right hand. In the next shot, it is now in her left hand. A blue mug is in her right hand instead. (00:05:15)
Continuity mistake: When Castle and Beckett go to question Jeffrey McGuigan, Beckett raises her badge twice: once while the camera is on Guy Wilson, and a second time when the shot cuts and the camera is on Stana Katic. (00:25:15)
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)
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)
In the Belly of the Beast - S6-E17
Continuity mistake: After Beckett gets back from her assassination assignment, she washes up in a bathroom and places the gun she was given in her front waistband near her stomach. Then she goes to meet Lazarus (Vulcan Simmons) in the basement, who realizes she's Beckett. When she pulls out the gun, she reaches behind her back to get it. (00:27:25 - 00:31:00)
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.
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.