Continuity mistake: When Castle comes home to Sophia waiting for him in his office, she is holding the Derrick Storm graphic novel; it keeps changing from open, to closed, even to her closing it every time we see it in her hands. It's very noticeable.
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.
Cloudy with a Chance of Murder - S5-E2
Continuity mistake: When Beckett is trying to get dressed for work at the beginning, she takes off a blouse she deems unsuitable and the bullet scar on her chest, which is usually at the start of her cleavage line, is missing. (00:00:25)
Cloudy with a Chance of Murder - S5-E2
Continuity mistake: When Beckett, Ryan, and Esposito are discussing Castle's date with Kristina Cottera, Beckett's fork is full of food in a long shot, which disappears in the following close-up without her eating anything. (00:32:15)
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: 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)
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 Beckett watches the weird/creepy video and a few images after seeing the ghost at the house, she hears a little girl laugh. However when Castle watched the video, that laugh happened at the moment with the ghost at the house, not after.
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)
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: At the end, Beckett spills coffee on the letter. In the first shot, before she frantically blots the spilled coffee, it says that the writer is "a junior at P.S. 370." Afterwards, this has changed to "P.S. 311." (00:40:40)
Like Father, Like Daughter - S6-E7
Continuity mistake: When Castle and Alexis visit Frank at the prison in Pennsylvania, as he's brought in, the guard removes his handcuffs. In one shot, Frank's arms are flat on the table, and in the following shot, his left arm is raised. (00:08:20)
Continuity mistake: When Kate gets a call from Lanie who asks her to come down to the morgue, Kate's jacket is beige. When Kate enters the morgue, it's black/dark blue. (00:07:40)
The Good, the Bad & the Baby - S6-E10
Continuity mistake: When Lanie arrives at the precinct to check on the baby, her shirt is tucked into her jeans, as seen when she bends over to pick the baby up. When the shot changes to behind Lanie, her shirt is untucked, and then when the shot changes to the front of Lanie, her shirt is tucked in again.
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)
Continuity mistake: In the flashback of Beckett and Montgomery, when Montgomery finds her in the archive room studying her mother's murder case, Beckett says that she was unable to find any leads worth following. But in season three, when Montgomery explains to Castle that that encounter was when he first met Kate, he says "she found some things that didn't add up", suggesting that she did find a clue worth investigating.
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...
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.