Continuity mistake: In the Moscow car chase, Bourne's car is hit from the driver's side by a patrol car. The driver's side window breaks. In the next few shots, you do not see any broken glass on Bourne. In the very next shot the car is not damaged on the driver's side.
Continuity mistake: In the Moscow car chase, when Bourne's car is hit by a FSB Mercedes which had been hit by a truck, the whole exhaust section of his vehicle is seen collapsing to the ground. In the next shot, the exhaust section is perfect.
Continuity mistake: After escaping interrogation Bourne switches SIM cards and throws the phone back down with it facing down. When we see the American awake the phone is now facing upwards.
Revealing mistake: When the demonstration crowd is assembling in the plaza, there's a yellow tram entering on the left hand side. Watch as someone walks across the tracks in front of it and disappears through the corner of the cab. The shot must be a composite of the crowd amassing and the tram shot separately and then overlayed.
Continuity mistake: When the assassin is following Bourne in Moscow, he stops on a bridge and shoots at Bourne, a second later, when the Moscow police arrive to detain him, his car is not on the bridge anymore.
Continuity mistake: During the scene where Jason Bourne interrogates the girl from Paris in a tram tunnel, her hair keeps changing from camera angle to camera angle. In one angle, it's off her face; in another angle, it's disheveled and covers the right side of her face.
Continuity mistake: When being pursued by the Russian agent in India, the girl is shot through the rear window of the vehicle. Yet when the vehicle is pulled out of the river, the rear glass is intact.
Factual error: When Bourne is tapping into the phone of the American consulate investigator, the display of his Siemens cell phone shows Pamela Landy's phone number as an incoming call, giving him the option to reply or reject the call. But at this point, they have already been talking for a while.
Continuity mistake: In the chase scene toward the end, both Bourne's and the assassin's vehicles are racing down a tunnel. Both of them run several cars off the road while passing them, which should block traffic behind them. Instead, in one long shot of the tunnel, a ton of moving cars can still be seen directly behind them in the tunnel as if traffic was completely normal. Furthermore, even if there was room to drive around the obstructions, nobody thinks it's a good idea to back off from two cars smashing into things?
Factual error: When Bourne arrives in Moscow at Kievskii station, he goes to check the address of the dead Russian reformer's daughter, looking in a phone booth yellow pages. There are no phone books, much less yellow pages, in Moscow phone booths.
Factual error: During the chase in Moscow, just after Bourne is shot in the shoulder, the Russian assassin runs down a subway entrance, but this is really at Berlin Alexanderplatz. In the background is the Kongresshalle, located just next to the Alexanderplatz, and there is in fact a U-Bahn entrance opposite it.
Factual error: While supposedly being in Moscow, Bourne really gets chased past the German Foreign Ministry. This is a landmark building. A picture of the building, same perspective as in the movie, is found here: http://www.stadtentwicklung.berlin.de/pix/baubilanz/regierungsgebaeude/auswaertiges_amt.jpg