Continuity mistake: When the two cops pull the stripper over, their car stops in the middle of the road. When Beck and Gallagher pass them later, however, their car is closer to the pavement. Their car moves yet again when Beck looks back at them out of his window. Also notice that three headlights are now on, including one that the stripper blew out.
Continuity mistake: When Beck and Gallagher are chasing the stripper (Claudia Christian) Gallagher shoots out the wheel of the stripper's car, which then proceeds to crash into a mannequin warehouse. As Beck and Gallagher approach the suspect's car there is the head and hair of a mannequin showing out the broken back window. Obviously from when Claudia Christian crashed into the warehouse. However the front car windscreen is unbroken as Beck passes it. So how did the mannequin enter the car?
Continuity mistake: When DeVries gets out of the Ferrari covered in blood, Willis is seen pointing a pistol at him. When the police blow up the car, he is using a shotgun. In fact, when they blow up the car, most of the images used are the same shots of them firing at the car before it hit the roadblock, only they're flipped. Willis also appears to switch from a right handed shooting stance with the pistol to a left handed shooting stance with the shotgun.
Continuity mistake: When DeVries is being chased by the cops, he passes some roadworks. At first there is only one wooden barrier in his way, with a workman about to position another one. The next shot shows two in place. DeVries appears to knock these over, but in the following shot he only hits one, with the other one transported to his left, ready for the cops to knock over.
Plot hole: When Gallagher is trying to kill the senator at the end, he is fired on by his bodyguards. Yet when they finally catch up with him, they're quite content to stand back and watch him torch the senator. One of them even lowers his gun. They couldn't have known Gallagher and the senator were aliens.
Continuity mistake: When DeVries' Ferrari crashes into the fence, the license plate is lying crooked, touching the bumper. When the cops blow it up, it's not touching the bumper. Also notice that the petrol tank and exhausts have been removed, revealing that the car blows up by explosives rather than police gunfire.
Continuity mistake: When the Ferrari boss calls Eddie to help deal with Miller, two guys wearing suits are standing in the sunshine next to a grey car. When Miller refuses to take no for an answer after being thrown out, you can see that the guys are gone and the car is now covered by a shadow. The red Ferrari also now has a longer shadow.
Other mistake: During one of the early investigations of the murder in the record store, there is a scene of the FBI agent and the detective in a Porsche driving through an intersection, almost crashing into a yellow car entering the intersection and swerving away to avoid an accident. Later on in the movie, there is another scene of the Porsche going through the same intersection, at a different angle, and almost hitting, again, the same yellow car, at the same position, doing the same manuever to avoid a crash.