When Alex escapes his "freejack"-ing, just after his visit to Julie's old apartment, the "Welcome to New-York" digital billboard shows Thursday, November 23rd, 2009. Nov. 23, 2009 is a Monday.
When Alex is escaping by car from Julies apartment, a car is turned over when it collides with a "tram". In the background, you can see the ramp.
When Alex is fleeing from Vacendak right after Julie Redlun first encounters Alex in the year 2009, Alex rams a car chasing him and then turns sharply to throw a random bad guy from the hood. As he makes the turn, the camera shows him shifting using a manual transmission in the center console and engaging the clutch, but when he throws the car back into gear it shows a shot of an vehicle with an automatic transmission with the shifter on the side of the steering column.
During the chase scene and after he goes under the trailer, Alex's vehicle changes from a full-sized Chevy truck to a smaller S10 truck.
Before Alex crashes the truck (and just as he's jumping from the truck into the river, it is clear that he's not really driving, it was all shot against a green screen. Some of the giveaways to this are:
1) There is no wind blowing Alex's hair
2) The lighting changes from the action shot, to the over the shoulder shot of Alex.
3) There are no reflections of the passing bridge structures and cables.
When the 2 motorcycles start to chase Alex, both of the motorbike starts as Honda 750 VFR and, when on crash, they are suddenly Kawasaki 500 Ninja.
On their way down in the elevator after leaving Michelette's office, Alex pulls the clip from his pistol and says "One shot left". During normal use, a semi-automatic pistol with one round left in the magazine will have TWO total shots remaining, including the round already in the chamber. If Alex had only one shot left the pistol magazine should have been empty.
Before Alex is 'freejacked' his fire suit does not have 'Champion' spark plugs patches on it. After he is 'freejacked' they appear on his suit. As he was introduced to (and spurned) the Champion rep regarding sponsorship just before the race, he wouldn't have been wearing a Champion patch in the first place.
Several times during the film a character holds a double barreled shotgun and a pump sound effect is heard. Double barreled shotguns do not have pumps.
When Julie is driving the red armored personnel carrier, exterior shots have her in the right seat. Interior shots have her sitting in the left seat.
In the warehouse Alex drops his weapon after he gets disarmed by a soldier and raises both his hands. When he escapes 3 seconds later, he is using his pistol but wasn't seen bending over picking it up off the ground.
The locker that Alex knocks over when being chased in the building is not there a moment later.
The position of the dead man's head changes when it's looked by Alex or by Vacendak.
Both Alex and Julie have completely different hairstyles between the time just before Alex goes into the sponsors' tent with Brad, and the time of the actual race. Alex goes from a flatter hairstyle to an obviously moussed or gelled one, and Julie goes from a long ponytail with bangs to a shorter, curlier style with no bangs (more resembling the style she has later in the movie).