Continuity mistake: When the two teenagers are down in Norman's fruit cellar, and a "lady" with a knife is chasing the boy, he leaves finger markings on the fogged up window. But by the next shot they have changed. You can tell because when the boy made the markings, his thumb and his index finger markings intersected, but when the camera angle changes the finger prints don't intersect and they are noticeably straightened also.
Continuity mistake: When Norman arrives home, he is startled by a note that is found beside the phone and he accidentally knocks his suitcase down the stairs and most of his clothes land on the top of the stairs. But as the camera angle switches to the bottom of the stairs, the clothes are further down the staircase. They couldn't have moved as they were stationary at the end of the other shot.
Continuity mistake: Norman picks up the note from his "mother" on the order wheel at the diner. He reads it then drops it on the floor. You can see it on the floor yet it's gone when everyone goes back in the kitchen. So where did it go? All the employees were out of the kitchen.