Byer says that he found the video of the Treadstone/Outcome bosses at a party on "YouTube." The Bourne Legacy takes place concurrently with The Bourne Ultimatum, which based on date references in the previous films is set no later than February 2005. The first video was not uploaded to YouTube until April that year.
While waiting in the airport to fly to Manila, Dr. Marta Shearing walks over to a newsstand and glances at a USA Today paper about the lab she worked at. The headline next to it read "Tablets Take PC Evolution To Next Level". This was a headline from 2011, but the events of this movie are occurring at the same time that "The Bourne Ultimatum" takes, place, which was no later than early 2005.
This film is set no later than February 2005, however in the movie, the song by Rodney Atkins "Cleaning This Gun" is playing on the radio. That song was not recorded until 2006 and was not released until 2007.
The location of Aaron Cross at the wilderness outpost as seen on the display at Drone Command is 61 48 28.54 -142 49 06.17 (or 61.632507,-142.968292), which has an altitude of 8900 feet. The aviation chart seen on the same display, which shows Aaron's tracker beacon, lists the latitude as 66°, not 61°. It also lists a Minimum Obstacle Clearance Altitude of 4600 feet (which would be underground if the drone is flying at the beacon's coordinates).
To apprehend Aaron Cross and Marta Shearing, LARX #3 commandeers a parked Manila police patrol car, a Toyota Corolla. But when he swerves into a busy street, the patrol car is now a bigger Toyota Camry.
As already mentioned, there is a goof in the planes used to escape after the attempted drone execution. The initial plane shown flying up the river gorge has a tail id of N7241q, which is a Beech Bonanza A33, single engine. From the cockpit, you can see it is a twin engine with winglets. Them the fly out scene end shows a twin engine without winglets. There were at least 3 different aircraft used in that scene, I guess we weren't supposed to notices.
Near the end of the movie, while addressing an oversight committee, Noah Vosen says "We had a problem with Treadstone six years ago." The Legacy story runs concurrently with the Ultimatum story in the Bourne timeline, and both of these stories take place in a time frame within the last few minutes of Supremacy. Supremacy takes place two years after Identity. Therefore the whole Bourne timeline so far comprises only two years, or slightly over two years.
During the pursuit of Cross and Dr. Shearing, it's mentioned in the operations room that they took American Airlines flight 167 from JFK to Manila. However, American Airlines flight 167 actually goes from JFK to Tokyo's Narita airport.
In the film, Shearing and Cross take a direct flight from New York's JFK Airport to Manila via American Airlines. In real life, there are no direct nonstop flights from New York to Manila, and American Airlines does not have any flights to Manila.
In the climactic car chase in Manila, LARX #3 is seen driving a Manila police patrol car, a Toyota Camry. The Camry, priced as a near-luxury car in the Philippines, has never been in the fleet of the Manila police.