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.
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.
Revealing mistake: In the scene where Jack has come back into the bus from being underneath it, he is talking to Annie about losing gas, if you watch closely he says "Mac" without pressing his button to call him first, then in another shot you see him press it when he starts talking to Mac.
Revealing mistake: In the scene in the subway Denis Hopper has again used an explosive jacket like that used at the start of the film, which is detonated if the remote trigger is released. However when on the subway train, Denis takes the remote back from Sandra Bullock and it is seen that the trigger is quite obviously released and Denis pushes it back in.
Revealing mistake: The Boeing 707 freighter that gets blown up by the bus bomb is obviously a "scrapped" plane (A plane that has lived out it's usefulness and is being readied to be scrapped). One good way of telling this is the plane's exterior shows heavy weathering wear from being stored a long time. But someone told me the way it looks could also be a hasty paint job using ordinary house paint. Either way, still something to look for.
Revealing mistake: When Jack is under the bus attempting to dismantle the bomb, if you look closely, when the cable comes off the hook, you get a shot of Norwood and the Lieutenant standing on the edge of the van holding the cable - you can see that it's their stunt doubles standing there.