Trivia: When Terry is being introduced, he drives up on his scooter, and has quite a bit of trouble parking it. This is because Charles Martin Smith actually didn't know how to drive a stick shift. The small accident he has is real, you can see him crash, look up towards the camera (at Lucas), and continue the scene. Lucas motioned for him to continue, because the crash looked so interesting.
Trivia: Harrison Ford wears a white cowboy hat in the film, because George Lucas wanted him to get his hair cut in the 1950's "crewcut" fashion. Ford didn't want to because it was in style to have longer hair at the time and he was afraid it would affect future acting jobs if he cut it. He convinced Lucas to just let him wear the hat to cover his hair.
Trivia: The entire movie was filmed over a span of about 29 consecutive days, and George Lucas generally didn't allow scenes to be re-shot if they came out plausible. Thus, entire scenes in the movie have botched lines and ad-libbed parts, the best of which probably being Toad's boasting about Milner's racing ability after Falfa rolls his car: Charlie Martin Smith couldn't remember most of his lines when they shot this scene, and made almost all of them up on the spot.
Trivia: Lucas actually had sort of an affinity for mistakes in this film. There were several instances where he would keep filming shot after shot until the actors would mess something up. Such as when when the guy leaves the liquor store and tosses the bottle to Terry, he stumbles and just about loses the bottle. Or when Terry goes back to the car, Debbie asks him "Did you get it? Did you get it?" but she noticeably flubs the lines up. Or even when the actor who plays Terry couldn't properly handle the motor scooter and has a small accident. These are instances where Lucas had many perfect takes of these scenes, but he kept the ones with mistakes in them to give the movie a more realistic feel.
Trivia: On Discovery Channel's "Mythbusters", it was proved that ripping the rear axle out of the police car was impossible without removing bolts and fixings.