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).
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.
Answer: Knowing Bourne, he must have had a keycard on his person. Remember that Landy guided Bourne back to the CIA New York Headquarters; she could have easily slipped a keycard in the Taxi Cab when Bourne was being picked up at the airport. All he would have to do then is avoid being detected by using the fire exits (hence going through the back).
Jason Riley