Revealing mistake: In the scene before they jump the gap, they played the film in fast forward to make the bus appear to be going faster. If you watch the police on the truck in the background, they are moving in fast forward as well.
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".
Continuity mistake: When Jack tries to get on the bus on the highway, he hits the door window and breaks it with his elbow. Later, when he finally catches up with the bus and gets on from the moving car, the door window is intact. Several times later it is visible, no break. Then later, when the bus is on the freeway, the glass is shown broken again, but in a different pattern.
Plot hole: If Jack can speed the train up, why does he not try to slow it down? Even if it can't be stopped completely, using the speed lever to reduce it to the minimum possible would be a sensible course of action. There is nothing to suggest he wouldn't be able to do this as he is able to increase the speed without any trouble. If there was something to show that slowing down the train would be unworkable it would make sense, but seems to more serve as a plot device.
Factual error: When the bus is driving over the gap in the freeway, it jumps off at an angle. And when it lands, it lands close to perfection. If the bus landed at the same angle it jumped off on, the bus would either tip over or the 2 tyres would burst.
Revealing mistake: After the first bus is blown up, if you look closely there is a truck with a chain pulling the burning bus. (Not really visible on DVD - think it was cleaned up.)
Continuity mistake: When Dennis Hopper psyches the police chief out by making him think he's on the third floor, the elevator clicks one too many times. The camera shows the numbers: "5, click, 4, click" then it switches to the police chief, during which time you hear another click. It then switches back to the numbers: "3, click." Shouldn't it be on floor 2?
Audio problem: In the scene when Jack tells the bad guy he wants to get of the bus, he says "it’s not against the rules". The bad guy then says "All right, but I want you back real fast". Look at his mouth while he says the line. You can clearly see that the talking isn't similar to the moving mouth.
Continuity mistake: When they run onto the roof near the start, there's another trooper behind Harry running onto the roof (only visible in widescreen - in 4:3 it looks like a weird reflection). In the following shot of Keanu Reeves you can see the reflections of Harry and the other guy on the plastic covering the scaffolding. We're led to believe that Harry and Jack should be the only ones up there, as everyone else has a job to do. Aside from those two shots, this third trooper disappears once they start hooking the crane up.
Visible crew/equipment: When the police officers are attempting to rescue all the passengers on the bus while at the airport by driving up beside the bus, at one point you get a front camera angle shot showing the people jumping out of the bus onto the police vehicle. If you look closely, you can see the camera man sitting on his chair reflected in the window of the open bus door, he is wearing a white shirt with sunglasses.
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.
Character mistake: At the airport, when Jack is under the bus on the trolley being towed by the truck, an accident causes all the cable on the winch reel to pay out. At this point all that's holding the cable to the reel is a small metal clamp. Jack slews around under the bus for a while, in grave danger of being run over by the vehicle's rear wheels, and then the clamp gives way (in slow motion). The now-free cable shoots toward the bus, and Jack pulls himself off the trolley just as it goes under the rear wheel. If you look at the shot where the cable is flying toward the bus, you can see two SWAT guys standing on the back of the truck, on either side of the winch. Their posture is completely relaxed and casual. Considering that for the past several seconds, Jack has been sliding around under the bus, fighting for his life, wouldn't the SWAT guys be much more excited--moving around, trying to get a better look, giving instructions to the truck's driver?