When Duke's girlfriend is struggling with the locked ice machine, we see Norman walk past her to unlock it. But we never hear nor see him actually unlock it.
He just lifts the lid.
When Norman & Maureen return from the restaurant, it is raining. They walk out of the cab, and get soaking wet. Moments later they go into Maureen's room, and in the next scene Maureen's hair is dry.
When Norman makes his beeline to Duke's cabin in search of his mother, it is still daylight (albeit cloudy and gloomy)
A moment later when Norman opens the door, it is dark outside.
During the beginning of the film, it is raining very heavily. However, when the grounds around the Bates Motel is shown, the ground is extremely dry.
On arrival back from the restaurant, the light in Mrs Bates' bedroom is on. However, when Maureen looks towards it and sees the figure at the window, the light is off.
The fingerprints from the boy killed in part 2 are shown to still be on the window in the cellar. Miss Spool cleaned them up before the police came (which Mary claimed to have done.)
A closeup shot of the roof on Norman's porch shows leaves blowing all over, but there are no trees next to the house, and none tall enough anywhere on the property.
When the female reporter gets inside the Bates house, she finds Maureen lying dead on the sofa in the parlor, but Maureen is still breathing.
Close examination of the newspaper on Norman's kitchen table near the beginning of the film ("Emma Spool still missing") reveals that identical random paragraphs of text are repeated in adjacent articles.
When the flashback of Norman and Mrs. Spool is shown, we see Norman hit her on the back of the head with a shovel. As he does this, we see the shovel wiggle up and down, indicating it is a prop.
When Maureen goes to see Norman at home for the last time, she asks him a question while they are at the top of the stairs. We hear Norman answer her, but his mouth never moves.
When Duke first arrives at The Bates Motel, he is talking to Norman at his car while holding keys between his teeth. Duke says "You live up there, eh?" but his lips never move.
After the police arrive at the motel to question Norman about a guest's disappearance & Marie asks Tracy if there's something wrong with Norman, Duke is standing in the doorway of the office. For a brief second, you can see someone(possibly a crew member) move a window curtain that's on the other side of the closed door going into the parlor.
The Bates Motel address and phone number are both show during a scene indicating it's on California Highway 113 and the area code is 805. Fairvale is a fictional town which is located out in the desert somewhere in Kern County, California. California State Route 113 runs from Solano County to Sutter County which there is no desert through that section of California's Central Valley. And the 805 area code is on the coast from San Luis Obispo County to Ventura County, which are both far away from the deserts in California.
When the reporter Tracy is shown Mrs. Spool's apartment, the manager tells her that the police have already paraded through the apartment. Yet there is mail and a notepad by the phone and magazines with many phone numbers on the covers. It is inconceivable that the police did not take these items in order to get answers to Mrs. Spool's disappearance, especially since one of the phone numbers was for Bates Motel, obviously linking Norman to her.
It is never made clear why Norman, after "Mother" kills Red in the phone booth, would have lifted the five dollar bill off her, which Duke gave to her, which he also previously stole when overcharging Maureen for a room, and then put it into his cash drawer.