Factual error: In Oregon and New Jersey, state law requires that a gas station attendant pump the gas. Romero pulls into an Oregon gas station and encounters a nosey person. They are both pumping their own gas.
The Convergence of the Twain - S5-E2
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.
Suggested correction: Norma doesn't die 2 weeks after they move to Pineview, she dies roughly 2 years later. Dylan & Emma have a baby, then in later scenes a 2/3 year old child.
Pineview Institute is the mental hospital Norman enters (during season 4) and they say he's 18 and has to sign the consent forms. Then at the end of season 4, Norman kills his mother (Norma), which is about 2 weeks later. The city the Bates moved to is White Pine Bay. In season 5 (which is set 2 years after season 4 ends) every time we see Norma, it's Norman hallucinating as she's already dead.
She didn't die two weeks after she moved to white pine bay, she died two weeks after she got married to Alex.
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.
Other mistake: When Norman and Madeleine are talking outside the Motel about Sam, the left side of the screen appears to be split down the middle after Norman says "Because you know it's safe to tell me", causing a weird effect on the chair that Madeleine is sitting in.
Continuity mistake: When Emma is talking with Caleb in the kitchen, the slice of cake in front of Caleb keeps moving between shots.
Revealing mistake: When Caleb visits Emma and Dylan, Caleb holds baby Kate. When he gives her back to Dylan, the baby is a doll.
The Convergence of the Twain - S5-E2
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)
