9 minutes into the film, as the elevator door closes, the last Passenger puts his arm in the way to stop it, but it is not visible in the mirror. This reveals that, to avoid revealing the camera in the mirror, they superimposed video into the scene.
The Mechanic opens the roof hatch on the elevator to help calm down the Guard since he is claustrophobic. However these hatches are always locked from the outside, the point of the hatch is not to allow passengers to get out in an emergency but to allow rescue personnel into the elevator. The last thing emergency personnel want in this situation is panicked passengers climbing around on top of the elevator or even worse trying to climb around inside the elevator shaft.
When the security staff tell them in the elevator that they will be switching off the lights. Despite the fact that there is only one way communication, the passengers start shouting and get panicked and the security man tells them it's OK folks no need to panic we just want you to know what's going to happen next.
The goof items below may give away important plot points.
When the salesman dies in the elevator, Detective Bowden gets on his radio and says "we have a possible 187." 187 is the California penal code section for homicide. This movie is set in Philadelphia and there is no penal code section 187 in Pennsylvania.
In the scene where Tony has a flashback to when he crashed the car into Detective Bowman's wife and kid, you can see that when the car spins into the ditch, the license plate is backwards, meaning that the clip was reversed.