Revealing mistake: In the scene where Norman visits Caleb at the motel on his own, after hearing Norma and Dylan argue, he gets into an argument with Caleb. Norman then pulls a knife out high above his head, at which point you see it is a prop/rubber type knife. The handle aimed at Caleb but the force Freddie Highmore has used to pull the knife up and back causes the blade to bend and aim toward the ceiling.
Deliberate mistake: It often rains on the show (it being Oregon, naturally), but never on the characters. Rain can frequently be seen against lights in the background of scenes, and not in the foreground.
Other mistake: After the scene where Norman texts Bradley that he is coming over, the next shot is Norman looking at the small transcript of his messages to her. If you look, you can see that the transcript starts at 2:34 PM. However, it's nighttime. You can even see the time says 2:34 PM at the top of the phone screen. Also, the original text of 'Hey' is missing although he texted her immediately after receiving it with 'I want to come over and see you.'
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.
Revealing mistake: At the beginning of the episode when Emma is talking with Norman, she drops the newspaper (of Bradley) in front of him. If you pause it and read the newspaper you can see the text has been repeated once for the text about Bradley and many more times for the news item below that.
Audio problem: After Deputy Lin drops the line "we'll get the results back fast," Sheriff Alex Romero responds with "I'm not sure how much nail clippings are gonna tell us." As he sits down, his mouth movement matches the audio, but when the angle changes, his mouth isn't moving at all.
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.
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.