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 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.
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: 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.
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.
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.
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: 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.