Factual error: If you look at the loop Keanu hooks the crane onto on top of the lift you can see that it and its bracket have been recently welded on (by the black residue it leaves), obviously because the lift itself didn't have such a loop. Even if such a feature existed, it wouldn't be simply spot welded on the top as this one is, it would need to be part of the lift's structure if it were to serve any purpose in supporting it in an emergency.
Revealing mistake: In the scene where Payne is waiting for the money to be dropped into the bin, he looks through the blinds out onto the street. When he lifts up the blind with his 'bad' hand, you can see his fingers and thumb taped up out of the way.
Revealing mistake: In the scene where Jack and Annie escape from beneath the bus via a trap door, the shot of them skidding across the runway shows a ring on Jack's left hand as it is wrapped around Annie. Jack is not married in the movie, but his stunt double must be.
Visible crew/equipment: When the bus is jumping the gap in the bridge, if you look closely in one shot, Sandra Bullock is not driving. Instead it's a large man that appears to be wearing women's attire.
Continuity mistake: Just after the bus driver has been unloaded and Helen tries to get off, Annie shouts "No Helen" at which point Jack turns around and grabs her shoulder to stop her. The shot switches to Dennis Hopper watching TV and then back to the bus where Jack is no longer even close to Helen when the bomb detonates.
Revealing mistake: As the first bus explodes on its way from the cafe, we can see a blonde pedestrian casually walk past a window with her ears covered. At no point does she even stop to glance at the burning wreck. It seems (from her perspective) as though the explosion were merely an inconvenient loud noise and nothing worth noticing.
Continuity mistake: When Annie drives onto the shoulder, after Jack has come out from investigating the bomb underneath, the bus crashes into a car on a tow truck. In the first shot the tow truck is well inside the white line on the road and it looks like it's half on the grass as well. In the following shot when the bus hits the car, the tow truck has moved to its left and is now on the white line on the road.
Continuity mistake: Just before the first bus explodes, Jack leaves the cafe and puts his coffee cup onto the top of his car. When he runs back to his car, the coffee cup is different as well as in a different position.