Revealing mistake: When John is escaping at the start, he throws a sharp left when a taxi appears ahead of him. Just before he takes the turn, we see a view from in the car. In this shot, you can see skid marks already ahead of him exactly where he's about to skid. (00:08:20)
Revealing mistake: In the beginning of the movie, when John get his Mustang, he starts accelerating deliberately to hit one of the cars (black sedan), but right after the odometer scene (where you see the gas going up) you actually see the car is stopped. It is pretty obvious. (00:09:30)
Answer: String Quartet in A Major, Op. 55, No. 1, by Joseph Haydn.