Continuity: When Bourne says goodbye to Marie when it is snowing, the snowflakes in Marie's hair changes between shots.
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Mistakes
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. See more...
The Bourne Identity mistakes
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.
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.