Revealing mistake: If you look at the missing part of the bridge, and look at the shadow underneath, the shadow is of a full bridge.
Visible crew/equipment: When the bus is about to jump the bridge, you can see that the bridge is flat, apart from the broken part, but when the bus jumps over the bridge, there's wood and stuff piled up at the end, making it "kick".
Revealing mistake: After the first bus explosion when Jack answers the phone, he looks at his watch, which shows 8:05 a.m. If you look closely the watch is on alarm, not regular time.
Visible crew/equipment: When the bus is turning right off the freeway at the start of the film, one shot shows a camera mounted on the side of the bus.
Other mistake: Towards the end when Dennis Hopper is on the subway train with Sandra Bullock, he has a gun in one hand and the detonator in the other. However, when the camera cuts to a close-up of him handcuffing Sandra to the pole, both hands are empty. If he took his hand off the detonator, the explosives attached to Sandra should've exploded, but they didn't. In the next shot, both items are back in his hand.
Revealing mistake: When the train is sliding along the ground near the end, there are sparks coming from the underneath (supposedly where the metal scrapes the pavement). Look more closely, and you can see that the sparks are coming from a bit of the train that's not touching the pavement anywhere.
Continuity mistake: After Keanu commandeers the civilian's car, breaks off the door and jumps to the bus the civilian loses control and heads for the water barrels in front of the divider. Right before he hits you can already see water all over his windshield.
Revealing mistake: During the rescue of the elevator passengers at the start of the movie, when coaxing the last woman out, there is a shot of the interior of the elevator where you can see the ground through the hole in the elevator floor, even though the elevator is still meant to be on the 22nd floor.