When Jason first meets Marie, outside of the Embassy, the amount of snow on the top of her car changes when the camera angle changes.
Jason goes into the train station and puts the red bag in a locker and leaves without the key. He never returns to the locker, but the red bag is back as is the money.
Close-ups of Marie holding the papers from the assassin's bag (when she examines the contents of the bag at the apartment and then in the car at the train station), the nails on the hands are long with clear polish, but Marie's nails are short with multi-colored dark polish.
When Jason parks the Mini in the underground car park, there's a wall to the right of the car. A few scenes later when the police find the car, there's a covered car to the right of the mini and no wall in sight.
When Jason opens the safe deposit box in the Gemeinschaft Bank in Zurich, the contents are spread evenly around the tray, with the heavy gun on the left. But the box had just been carried upright (by the handle) and set down on the table, so that the contents should all be in a heap on the right-hand side.
Bourne arranges to meet his boss on the bridge at 5:30 p.m. The farmhouse decorations indicate it's around Christmas time. At 5:30 p.m. in Paris in mid-winter, it would be almost, if not completely, dark.
The names on his Russian passport are written both in Cyrillic and Latin letters. In Cyrillic they say "Lshtshfum, Ashef" (which is a total nonsense - it is matching Russian letters from buttons on English keyboard), and in Latin letters it is "Kiniaev, Foma". (In the sequel The Bourne Supremacy (2004), his Russian passport correctly has "Kiniaev, Foma" in both scripts.)
The Russian passport is written in Russian and French, but refers to the "USSR". In French it should be written as "URSS"
The Russian passport in Jason's deposit box reads "Moscou" (French spelling) instead of "Moscow." Russian passports use English as a second language, not French, even for passports issued in Paris.
When Bourne goes to the consulate in Switzerland, they show a large number of Marines chasing after him. In reality the Swiss embassy has fewer than 6 Marines.
At the beginning, when the Italian sailors drop Jason off, he is seen walking away on the port. A car passes by, and he apparently vanishes. However, he can be seen running behind it, and his feet show on the reflection beneath it.
When escaping from the safe house Bourne jumps/falls down 5 floors of the building shooting one agent as he falls. He lands on top of the body of another agent before rolling away. getting up and exiting apparently uninjured. This fall would have been at least 15 - 20 meters and Bourne should have been killed or severely injured by the fall.
After cutting her hair, Marie and Jason begin to kiss. Jason's watch first appears on his left wrist. It then appears on his right wrist. The chronograph pushers are still closest to his hand, revealing that the image was reversed rather than the watch being on the wrong arm.
When Bourne escapes the Embassy onto the fire escape, the fire escape breaks free from the wall. The front of the platform is now higher near the door and would cause the door not to open. However, it's shown opening when the Marines look for him outside. When Bourne is climbing below the Embassy, the front of the platform can be seen to be blocking the door.
There is no snow at all on any surface higher than the second floor of the consulate, except for the sill Bourne is climbing on, and the fire escape.
In 2002, Bourne would not have been able to travel by train from Italy to Switzerland without ID. Switzerland did not sign the Schengen until 2004 and did not implement it until 2008.
It is supposed to be winter in Paris, but one evening shot showing a view of Paris has the sound of crickets.
After the assassin breaks through the window into Jason's apartment, he empties his submachine gun in three bursts. When the magazine is empty, a "click click click click click click click" is heard. In reality, when the weapon is out of ammunition, there would be one click only as the weapon is a Micro Galil and fires from a closed bolt with no bolt hold-open device.
When the assassins are coming up after Bourne has talked to his boss, the third assassin is seen inserting a new magazine into his rifle. However, the sound heard as he inserts the magazine is that of a round being chambered. Additionally, right before he is shot by Bourne as Bourne falls, he is heard to chamber another round. (This actuality would be correct at that point, as he hadn't chambered a round initially, only loaded a magazine.)
When Eamon is running away with Marie and his kids, the camera passes behind the car and a crewmember is reflected in the trunk.
When Bourne and Marie escape the police, there is a cameraman on the curve by the restaurant Merivan.
When Jason nearly falls off the ledge, the stunt double shows curly, shaggy hair which Bourne doesn't have.
Crew pulling dolly reflected in a car window as Bourne walks to the consulate.
During the car chase, when the yellow van tips over, a large lever used to flip the vehicle is clearly visible on its underside.
The chase in Paris follows a totally impossible way, mixing several famous spots like Place Vendôme, Montmartre, the Front de Seine and the quais near the Louvre. All those places are several km from each others and absolutely not seen in a possible order.
Jason Bourne seeks refuge in "U.S. Embassy Zurich". There is no U.S. Embassy or Consulate in Zurich. The Embassy is located in Bern, which is the de facto capital of Switzerland.
When fleeing from Paris, they stop by an Aral tank station, which exists in Germany but not France.
When Jason and Marie are driving from Zurich to Paris, they can be seen on a country road next to a railroad track with high mountains in the background. While it is true that between Zurich and Basel, the railroad track is at some points next to the road, they would certainly not have taken a country road. There are highways directly leading from Zurich via Basel to Paris. Furthermore, there are no mountains that high anywhere near the route they are taking. The only mountains that could possibly be seen by them is the Jura, which is no higher than 1720 meters. The mountains shown are however clearly supposed to be the Alps.
In the French countryside, an Eastern Wood Peewee can be heard in many of the outdoor scenes near the farmhouse. This bird is not indigenous to France.
Though rushing to close the Treadstone office in under 3 hours, they shred documents one page at a time.
Bourne is seemingly miraculously better only two weeks after sustaining two bullets to the back and being treated by a fisherman, without receiving professional medical care.
Bourne strikes Conklin repeatedly, but fails to take away his weapon, which Conklin having retrieved from the floor, points into the stairwell and could easily have shot Bourne.
When the fishing boat captain treats Bourne's wounds he checks his whole body and discovers the strange scar on his hip. But as this is a scar and not a wound requiring attention there is no reason for him to cut out the ID chip from his hip. The clues to Bourne's identity should never have been revealed from this. Bourne should leave the fishing boat with no clue to his identity and the film's writers would have had to find another way to reveal his identity.
It is left unclear how Nykwana Wombosi received the intel that John Michael Kane was responsible for the assassination attempt against him. It is possible that he questioned morgue workers about a man who supposedly was found drowned in the sea. However, Treadstone was spreading the narrative that Kane had been killed in a car accident. This is a plot development that would need to be dealt with.
When Bourne and Marie are about to abandon her car in the garage, Bourne says he'll wipe down the car (of fingerprints) but by then it is clear that it is known who they are so wiping the car clean would be a waste of time, something Bourne would know.
The wanted poster put together by Nikki (written in German) in Paris has grammatical and spelling errors all over it (ie. "Verhaftungsantrag" instead of the correct "Haftbefehl").
The two police officers who wake up Jason on the park bench in Zurich speak standard German with a strong Swiss German accent. They would have talked to Jason in Swiss German before perhaps switching to German once they realized that he was not Swiss.
Bourne at no time makes any effort to alter his appearance, yet expects Marie to cover, dye, and cut her hair oddly.
When Jason and Marie are at the farmhouse, the first two times Marie says Eamon's name, she mispronounces it as Ee-mon. The third time she says his name, she pronounces it the proper Irish way as Ay-mon.