Continuity mistake: At the police station, just after Cory was killed, the Chief of the precinct is looking at Joe and says "The same son of a b**ch saved the president's life." When the shot cuts to the other guy, then back to Joe and Jimmy outside the office, in the background the chief is now sitting back at his desk - some pretty quick moving between shots. (00:31:40)
Factual error: C4 needs a detonator or blasting cap to explode, and so wouldn't go off from being shot in the trunk of Joe's car. You can even set it on fire and it will just burn slowly. (00:44:35)
Factual error: Senator Calvin Baynard orders police officers to arrest Joe Hallenbeck for crank calling him. In California, a person can only be arrested for a misdemeanor if caught in the act by law enforcement. At the time, harassment (unless it was a threat) by telephone was only a misdemeanor. In 1996 it became a felony due to the passing of the Telecommunications Act Of 1996 signed into law by then-president Bill Clinton. (01:36:59)
Revealing mistake: When Mike Matthews' car explodes, it's a dummy in the car, not a person.
Plot hole: Marcone goes out into the parking lot, notices the white BMW, and then proceeds to shoot out the rear passenger window. Two problems with this scene, firstly, the front window is now perfectly intact when previously it was shot at during the limo chase, and secondly, Willis' character didn't even lock the car up, Marcones shooting of the window makes little sense with people around, which notably don't react to the shots at all. (01:21:05 - 01:31:15)
Continuity mistake: The whole car lands in the swimming pool, with the back end stuck up in the air and the front end down because of the weight of the engine. A couple of shots later with Darian and the pool owner on the phone, the car is now sat up on its front end, which is now propped up on the side of the pool. (01:18:55 - 01:19:45)