Anachronisms: During the Los Angeles home sequences, Claire's/Robbie's telephone number has a 310 area code, which was introduced November 2, 1991. The area code should be 213.
Anachronisms: The phone at the Peacocks house is too modern for the time - the cord going into the handset had a clip in cord versus being attached directly to the piece.
Errors made by characters (possibly deliberate errors by the filmmakers): During the sequence when Robbie and Claire buy the motorcycle, Robbie gets out of the car to sit on the motorcycle and even though he locks the car, he leaves the headlights on.
Revealing mistakes: Right after Jude leaves the Beatles and they are chased by fans, you can see the last person in the mob slow down immediately when they're behind the trellis.