Other mistake: After the early truck chase, Axel arrives at the police station. He walks through a glass door that reads 'Investigaton Operations Division' which is missing the last 'i' in the first word, exactly as I've typed it here. (00:08:10)
Continuity mistake: At the start of the film, Mahoney is wearing a white shirt with badges on it from the company he works for. When he's being interrogated by Sgt. Reed the shirt remains the same until the last part of the scene. The camera stays on Mahoney and we can see that the badges on the shirt are gone. If you look closely, you will notice that he is even wearing a completely different white shirt, which now looks more scruffy and creased. (00:08:00)