Rocco's car in the demolition derby changes halfway from a Buick to a Pontiac.
Early in the demolition derby, as Fonzie is backing his car up, you can see one of the Malachi's cars out of commission upright on its side, and the other Malachi car empty and idle away from the other cars.
The hairdryer that Joanie packed at Fonzie's request is not the same hairdryer Fonzie used in the demolition derby.
When Fonzie uses the hair dryer to blow the baby powder back to Rocco's face, there is no way the hair dryer could work without an electrical outlet.
Malachi brothers are shown using walkie-talkies to talk to each other during the demolition race. Transistorized walkie-talkies did not come out until the middle 1960s.