Character mistake: There is no way on earth that a police officer would shoot a hostage in the thigh to 'take them out of the equation'. Anyone who suggested such a thing would likely be taken out and shot themselves. Bullet wounds to the thigh are often fatal, as an injury to the femoral artery causes massive and frequently unstoppable blood loss. Breaking the femur often leads to fat embolisms as bone marrow gets into the bloodstream and then to the lungs. In fact a broken femur is a life threatening injury in itself, and a shattered femur - a typical bullet injury - would almost always result in a total amputation. You cannot aim carefully enough to avoid the bone or artery as their position in the body varies, (as will the bullet trajectory upon impact). Jack is an experienced cop and would know the potentially disastrous consequences of shooting someone in the thigh. He'd shoot him in the foot.
Continuity mistake: Early in the film, Jack shoots Harry through the left thigh (taking the hostage out of the equation). At the police awards ceremony, Harry is using a cane on his right side and his limp favors his right leg. After the ceremony, in the bar, when Harry gets drunk and starts to leave, he's using his cane on the left side and his limp favors his left leg.
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. (01:02:50)
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. (00:33:40)
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". (01:03:35)
Plot hole: If Jack can speed the train up at the end, 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.
Continuity mistake: At the airport the black sign on the side of the bus disappears for one shot. (01:09:00)
Revealing mistake: When the first bus is blowing up, in the shot of the right side of the bus as it's being engulfed in flames, look closely and you'll see the cable attached to the front of the bus, under its bumper, as it's slowly being pulled by the van in front of it (some DVD or Blu-ray versions may have been edited). (00:26:45)
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? (00:20:50)
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.
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. (00:11:30)
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.