Near the beginning of the drag race with Julie's hair on fire, in a wide shot from the front of the cars, Julie's friend can be seen with her sweater on Julie's head before she's seen taking off that sweater to put out the fire a few moments later.
When Dude lowers his head and uses his hair to make a grease slick at the skate park, his hair actually wipes up part the grease slick that it's supposed to be leaving behind (this is because the scene was actually shot with David Arquette running his head over an already-present grease slick).
Nixer: [trying to convince Dude not to go to the rumble]
I know you hate this town. I know you hate Teddy. I do, too. But I also know you love your music. So fight for what you love, not for what you hate.