Factual error: When the first assassin drives to Waterloo station to take out Simon Ross and Bourne, he is driving a BMW 3 series with a 2006 UK licence plate. However the events in this film are meant to follow on six weeks after the previous film, which make it still set in 2004.
Suggested correction: Nowhere in either of the first 3 Bourne films indicate the year they are taking place.
Technically, there is a timeline. You may have to watch the films again, and read up on when production for each film began and wrapped. The Bourne Identity was filmed between October 2000, and Spring/Summer 2001 (Greece scenes). Supremacy (With the exception of the New York ending which was filmed two weeks prior to the release) was filmed between October 2003, and March 2004 Ultimatum was filmed between October 2006 and March 2007 (which explains the snow seen in New York) Identity takes place in the winter of 2000, while Supremacy is set two years later, with Ultimatum taking place six weeks after he escaped Moscow. Legacy takes place around the same time as Ultimatum, and the last Bourne film (Jason Bourne) is set ten years after the events of the Supremacy/Ultimatum timeline.
The year of filming can't be used as indication of when films are set.
Revealing mistake: Right at the start, when all the police cars skid to a halt, there are tyre marks on the ground from previous takes. (00:00:30)
Other mistake: In the paper file regarding Project Blackbriar Jason Bourne's bloodtype is noted as A+, but on David Webb's dogtags it's O-. Since David Webb is his real identity, O- must be his real blood type. If Bourne was injured and known to have blood type A+ (as it is stated in the docs), the person treating him would believe he was capable of receiving A+, A-, O+ and O-. However, since his real blood type is O-, he is compatible with type O- exclusively. So this would mean a 75% chance of receiving the wrong blood type in an emergency.
Suggested correction: This is not a movie mistake. Documents made for a new identity would have details changed to mislead. Moreover, if he is wounded in the field and needs a transfusion, no-one is going to be searching for blood type on files, they'd use plasma, O - or do a test on the spot.
Other mistake: In the end credits, Gavin Greenaway, the conductor of the orchestral score, is credited as "Gravin Greenaway". (01:46:50)
Factual error: When Bourne googles Sewell and Marbury, the Sydney address that shows up has a lot of errors. The street number would not exist (too many digits), and the postcode is wrong (also too many digits). The phone number area code is also incorrect and does not include the country code (+61). (00:29:01 - 00:30:00)
Revealing mistake: When Bourne jumps through the glass window during the rooftop chase, it is very obvious that the glass shatters before Bourne crashes through it.
Revealing mistake: In the commentary, the director states that the crowds in Tangiers were real, not hired extras, and that therefore there was an effort to avoid having them look at the camera. However, when you can see the crowd walking up a street, their backs toward the camera, while one man (to the right) faces the camera while holding his cell phone up. He is obviously taking pictures of the camera crew, probably unaware of the fact that he is being filmed, as it seems the shot is filmed from afar. (01:01:50)
Continuity mistake: In Madrid Bourne calls the emergency line and says he's in 334 Norte street, which triggers cops to show up. When Bourne arrived at the building he looked at the door and it was a 2 digit number which one can faintly see it starts with a 1. (The filming location took place at number 10 Virgen de los Peligros street).
Factual error: The double decker bus in the Waterloo (York Road) scene has the number 43 on it. Paul Greengrass told the driver to put any number up on the front destination blind. The 43 does not go to Waterloo Station, but goes to London Bridge Station.
Character mistake: In London when Bourne runs down the escalators the camera follows him from behind. All the people act normal except for a man that turns around right when the camera man is about to pass by next to him.
Character mistake: When Simon Ross shows Interpol a picture of Jason and Marie together in the coffee shop to Ray Willis the photo shows Marie with a dark bob cut. She didn't get that cut until they were "on the run" and no agency would have had her looking like that. (00:06:48)
Character mistake: As Jason reads the Guardian Newspaper, he finds an article about himself entitled, "Who is Jason Bourne?" The caption for the article reads, "His code name is Jason Bourne, but he had many identities, each one seemingly more deadly then the next," instead of "more deadly than the next." (00:12:50)