Visible crew/equipment: When Marion arrives at the car dealership, the salesman sees her and starts walking towards her. If you look carefully, there is a wire trailing out his trouser leg, most likely for a hidden mic.
Revealing mistake: When Marion is driving her car through the night, she keeps looking at her speedometer. You can clearly see that the gear shift lever is in "park" as she is driving.
Factual error: When Janet Leigh is shown lying dead on the floor of the shower, there is a close-up of her open eye. The pupil is contracted to a pinpoint (obviously due to the bright lighting) where it should have been dilated. After the film was released, Hitchcock heard from several ophthalmologists who pointed this out and suggested he use belladonna eyedrops in the eyes of "dead" people in future films, as the chemical prevents the pupils from contracting.
Deliberate mistake: When Norman picks up Marion's body to carry it to his trunk, a bra is visible through the shower curtain. Gus Van Sant included this goof in his 1998 remake.
Revealing mistake: After Marion has been murdered there is a close-up of her face. If you look down to her neck you can see her pulse.
Continuity mistake: When Marion and Norman are talking after he has brought in some sandwiches, Marion tears the same piece of bread 3 times on different occasions.
Visible crew/equipment: When Marion is packing in her room, the camera is panning back over the bed to show the newspaper with the cash wrapped up in it. As the camera pans back, one can see the camera's shadow on the bed.
Continuity mistake: When Marion steps into the shower, we can hear (not see) her unwrap a bar of soap and throw the wrapper on the floor of the shower. But when Norman is cleaning the bathtub, after Marion is killed, the wrapper is no where in sight.
Revealing mistake: After Marion's sister and boyfriend look through the Number 1 bathroom and find the ring on the toilet, they turn off the light. On the wall behind them you can make out a square beam of light, but no other lights are on in the cabin.
Continuity mistake: As the camera zooms into the hotel window, you can see a shadow on the blinds. But in the next shot, the shadow is now longer (even though it's supposed to be in real time).
Factual error: The car she trades her car for in at the dealership is a used 1957 car, but when Norman is driving it into the swamp you can see on the license plate that the expiration year is 1956. It couldn't have a tag that expired before its model year.
Continuity mistake: In the shot in which Norman goes into the bathroom and puts the pail behind the door, the shower curtain rings are spread out. In the very next shot in which he emerges from behind the door, the rings are in tight groups. As he leaves the bathroom, the rings are spread out again.
Continuity mistake: After seeing Marion's dead body in the bathroom, Norman accidentally knocks down a framed picture of a bird (with the picture facing up and it is a few inches away from the wall). But when Norman is spreading the shower curtain on the floor, the picture has changed position (with the picture now facing down and it is against the wall).
Continuity mistake: When Marion arrives at the Bates motel, she sounds the car horn for the first time, the windscreen wipers are switched on. She gets out of the car, looks towards the old house, then goes back to the car, as she sounds the horn for the second time the windscreen wipers are now switched off.
Continuity mistake: When Mother Bates leaves the motel room after stabbing Marion, she leaves the room door wide open. When Norman reaches the door to check on Marion, the door is closed.