Audio problem: When Bourne rescues Marie, he fires a silenced pistol at the man who was trying to rape her, but the sound is of an unsilenced gun. (01:01:10)
Factual error: Shooting at a gas tank with buck shot at 50 meters distance will not make it explode (it likely won't even dent the surface), and lead pellets do not cause sparks when they hit.
Continuity mistake: When Bourne says goodbye to Marie when it is snowing, the snowflakes in Marie's hair changes between shots.
Factual error: Jason Bourne is supposed to be fluent in German, but he doesn't correctly pronounce a single German word in the film.
Continuity mistake: When Jason is trying to escape from the metal ledge in the US embassy, the ledge appears covered with snow A later shot from afar shows the ledge with the snow removed When the marines show up, the snow is back.