When Beckett and Castle go to the Peterson's residence, Claudia Peterson tells them that she tried to call Sara but the call went right to voice mail, indicating the phone was turned off. Later at the Richardson's apartment, Castle calls Sara's phone and it rings.
In the final scene, you see Castle typing on his laptop. He closes the laptop and puts it on his desk. Seconds later when he's looking at the photograph, you can see the laptop open again on the desk in the background. When the camera is panning out, it appears to be closed again.
When Ian Harris is interrogated, the ring on his right hand switches between middle and ring finger.
Chloe is cutting her leg, which is all bloody but there is no blood on the knife.
Assuming the basement is one floor below the ground floor the elevator travels 13 floors in 32 seconds. At that speed it only travels 2 floors in 5 seconds putting the Nanny on the 14th floor, not the 15th.
When Castle and Beckett are talking to Lanie over the corpse of the nanny, the dead girl's eye moves when we first see her.
When Castle and Beckett are entering the apartment building to investigate the time variance on the elevator tapes, the exterior shot shows a green canopy with "The Langham" and "715" to note the name of the building and street address. This is obviously The Langham in Los Angeles which is located at 715 S. Normandie Ave. in Koreatown. The Langham in New York is at 135 Central Park West.
Castle has written dozens of detective novels yet does not know police are allowed to lie to suspects during the course of an investigation.