Continuity mistake: Norma's headstone gives a year of death as 2015. It also gives Norman's birth year as 1995, making him 20 when she died, but it is repeatedly stated that Norman is 18 when he enters Pine view, and Norma died 2 weeks later.
Continuity mistake: When Norman is in Madeleine's shop, he picks up a chocolate chip cookie. We see him bite it, and we get a good look at the cookie. Then he sees Madeleine and begins talking to her. That is not the same cookie he had, because all of a sudden it has a huge chocolate chip near the top now...when it didn't before.
Continuity mistake: After Norman dismisses Norma's suspicion about him going to "another business meeting" as childish, he heads for the door - the sunlight from outside is flagrant as he opens it. In the next scene, Norman is seen entering his car, in the same outfit, and it is night time. (00:28:15)