Continuity mistake: When Jason is cutting Marie's hair in the hotel room, his watch is on his left wrist. When he and Marie begin to kiss, in this flipped shot Jason's watch is on his right wrist, his moles have changed sides, and the hand-held showerhead behind them is backwards as well. Next shot his watch is back on his left wrist. The flipped shot has nothing to do with the small bathroom mirror.
Continuity mistake: This is the scene where Jason is on the fire escape platform in the consulate in Zurich. Before he goes down below the platform we see that the platform is cleared of all the snow. Then moments later, when security guard opens the door and Jason is under the platform, the top of the platform is fully covered with snow again.
Continuity mistake: When Bourne approaches Marie about a ride, they talk across the top of her Mini. First, there is lots of snow on the car's roof. Then, there isn't.
Continuity mistake: When Bourne blows up the tank at the farmhouse, the wide shots show a solid wall of black smoke. In the closer shots there's nowhere near as much. The smoke in the first shot must be coming from the explosion, and in the closer shot we're looking right at the destroyed tank, so it can't be due to different angles.
Continuity mistake: In the part of the embassy scene where Matt Damon starts clobbering security people, the Marine's hat falls off no less than three times.
Visible crew/equipment: When Bourne is escaping from the Embassy and standing on the fire escape ledge, the safety cable for the later climbing scenes is clearly visible on the ledge around the corner to the right.
Revealing mistake: When Jason climbs onto the rail of the fire escape, it is not attached to the wall - intentionally, it has not broken - but then in another shot, two seconds later, it 'breaks'. It pulls out of a visible hole in the wall, although it was never actually attached and there was no hole before.
Visible crew/equipment: Right at the end of the car chase, the yellow van in the pile-up is flipped over by some kind of large metal lever in the undercarriage. This is seen from the last 2 angles of the crash.
Continuity mistake: When Matt Damon is on the boat, his gun shot wounds are on his left shoulder blade in a horizontal line. In the hotel scene when Marie is taking off his shirt, they are diagonal between his shoulder blades.