Plot hole: George Lebay says that his brother died "6 weeks ago" inside Christine and that's why he's selling it. Later that evening after Arnie leaves his house and goes to Darnell's, Will Darnell says he "knew a guy who owned a car like that" and "the bastard killed himself in it." If it's only been 6 weeks since his death, shouldn't Darnell have recognized the car? It's not like there were lots of red Plymouth Furies (custom order color) running around the small town, let alone the USA, even in 1978. (Also considering how production even had a hard time finding them for the movie).
Suggested correction: He says he knew a guy with a car like that. It doesn't have to be the same colour or even the same generation. Just a Plymouth Fury.
Darnell basically said he knew THE brother of Lebay, not just some guy who owned a similar car. Darnell described Lebay's brother based on the story. Again, it was him, not just some other guy.
Plot hole: The police let Norman back to his house on the same night multiple murders happened. He is even allowed into the fruit cellar, where most of them happened. (01:38:25)
Plot hole: It seems unlikely any mental institution would let a patient out to visit home for any length of time as happens in the movie with the killer and his mother.
Suggested correction: Unlikely, but still possible. Almost every workplace has a situation in which a person is bending the rules.