Factual error: When Claire pulls herself out of the bathtub, she falls right over the center of the tub. The bloody fingerprints would have been wiped away or completely smeared by her nightgown and bathrobe during the fall.
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.