Continuity mistake: There is one scene in the final earthquake as Ski and Sonny are driving around the city that's being destroyed - the Trans Am gets hit from the right side, hard enough to throw the car into a small skid, but seconds later there is no damage to the car, and nothing like that was discussed during the planning of the stunt. One has to wonder if that hit was unintentional and not scripted.
Continuity mistake: In the opening credits, we see Hooper putting on a pair of bulky hip pads and a back brace - the kind that wraps around your waist. He then puts on a pair of tight leather pants, but in the following shot as he is putting on his watch there is no brace whatsoever. There's no possibility that the brace was hidden under his pants; in a later scene the brace is visible even though he is wearing the same tight pants.
Audio problem: Right after Hooper says "Bye bye, nice officer." and activates the rocket system, the cop driving beside them screams "Great God almighty.". Watch the cop's rear view mirror when he yells that - it's a completely different person in the mirror and his mouth doesn't move at all, much less yell "Great God almighty." But when he calls "Headquarters. never mind", on the radio, the original cop is shown again.
Revealing mistake: In the scene where Cully injects Sonny in his back, you can see that just just after he pushes the plunger, the spring mechanism moves on the inside of the syringe. He is not actually injecting Sonny, but the needle retracts on a spring loaded mechanism into the syringe.