Continuity mistake: When Claire gets the box and necklace out of the lake, she sees the necklace and lays it down on the open box. She goes to get the phone and then Norman quickly appears. She then later has the necklace on in the tub.
Other mistake: When Claire turns the hot water valve with the chain, it's turned in the wrong direction. It was turned to open it more.
Factual error: In the end, the husband calls her friend and tells her to check on Claire at home. But he's calling from his home phone, so the police will know he was there.
Suggested correction: Norman tells Jody that he and Claire argued, and he is going to sleep at his lab. This is not necessarily suspicious. It sounds like he is on his way out the door, while Claire is upstairs, avoiding him or wanting to be alone after their argument.