Continuity mistake: After Hall has been shot in the leg in the simulation of LA 1937 the hole in his trousers and his injury disappear, as seen in the fight sequence at the pool. Hall even uses his leg to hit the bartender in the stomach, what would have made this very painful if he had been shot there.
Continuity mistake: At the beginning of the movie, Mr. Fuller writes a letter for Douglas Hall. When he finishes, he writes the name on it in a bold hand style. Later, when he gives the letter to the barman, the name on it is written with completely different, beautiful handwriting. When the barman opens the letter, we see that it now has a different style again.