The old red car with the white top is supposed to be a 1958 Plymouth Fury, the same make and model as Christine (1983).
When Alan asks his mother how his father died, she says he was hit by a car while walking along side the road (while on his way to get gas for his car). On June 19, 1999, Stephen King was struck (and almost killed) while walking along Route 5, in Lovell, Maine.
In the short story, George Staub's car was a Ford Mustang. The filmmakers decided to go with a red and white Plymouth as a nod to Stephen King's Christine. However, Christine was a 1958 Plymouth Fury and George's car was a 1960 Plymouth Fury.
While riding in the car with the farmer, Alan's inner self warns Alan about wishes. He says "Remember what happened with the monkey's paw." "The Monkey's Paw" is a story by W.W. Jacobs in which a cursed monkey's paw grants wishes with lethal consequences. It has been cited as an influence for Stephen King's "Pet Sematary" and was mentioned in other King books.