Continuity mistake: At the museum, Kate writes "Nuts" into her diary. A few seconds later she writes "Pick up turkey." and in the intervening period the word "Mints" has appeared below "Nuts". (00:14:40)
Continuity mistake: When Kate drops her glove, it lands with the fingers pointing towards the wall. When the man picks it up it has rotated by 90 degrees. (00:16:25 - 00:18:20)
Continuity mistake: Kate throws her other glove down onto the steps of the museum. When she walks down the steps towards the cab, the glove is not visible behind her. It should be on the square of stone that is above her left shoulder. (00:22:00)
Continuity mistake: Kate writes a note but then scribbles it out and pushes it to one side, next to the magazine on the table. In the next shot, she starts writing another note, and the first one has completely vanished. (00:29:40)
Continuity mistake: The amount of blood on Kate's face decreases between the time she is attacked and discovered. The pattern changes from shot to shot as well. (00:34:15)
Continuity mistake: While Dr. Elliot is being interviewed, there is a yellow piece of paper stuck to the window behind him. After Peter leaves and Detective Marino reenters the office, the paper has moved about a foot higher up. (00:46:10)
Continuity mistake: As Liz describes her nightmare to Dr. Elliott, she walks across his office gesturing with her hand to aid the description. The camera angle changes, and her hand is now in her pocket. (01:19:00)
Deliberate mistake: Has there ever been a more obvious body double than the one used for Angie Dickinson in the shower scene? Not only does the top of every shot stop right at the collarbones, she is much taller than Dickinson, she has a much deeper tan and (of course) her breasts are much, much bigger. In fact that is Victoria Johnson, Penthouse Pet of the Month for August, 1976.
Plot hole: After his mother's death, Peter sets a camera up outside her therapist's office, so he can see who goes in and who comes out; he thinks his mother's killer might be one of the doctor's patients - a tall woman with long blonde hair. All he sees is people going in and people coming out, and then he sees her - the tall blonde. Problem: He never saw her going in, only going out, which is critical, because the killer is the therapist - a tall man - wearing a long blonde wig and make-up. Of course no-one says anything about "We never saw her going in, only out, so it must be the therapist!"
Continuity mistake: When Liz is talking to the police and Dr. Elliott's psychiatrist after Dr. Elliott is shot, she gestures many times, showing that her hands are perfectly fine. How is this possible when Dr. Elliott slashed them? Even if this conversation takes place much later, she should still have a small bandage or signs of stitches.