Factual error: During the car chase scene with the Mustang, the driver of the Mustang repeatedly shifts his automatic transmission from "drive" to L1. Also, one shot during the chase shows that driver's feet using a clutch to shift his automatic.
Continuity mistake: When Doyle arrives at the dock at the beginning of the movie, we see Doyle from behind. A boy with a yellow shirt and a girl with a flower dress pass him on his right side. However, there is a change of shot, and now we see him from the front, and behind him we see the boy and the girl, but instead of being at his right side, they're at his left.
Factual error: The route to Tower Bridge is completely wrong - there are no duel carriageways approaching the bridge from the Tower of London side of the Thames, it's all single roads in that area.