Continuity mistake: When Amanda is first shown lying in bed, she is wearing her left shoe, but not the right. When she steps up onto the railing, the shoe is on her right foot, but this looks to be a mirror image, possibly on the sliding glass door - fair enough. But when she's lying on the roof of the car, she's wearing both shoes. (00:02:00)
Revealing mistake: A short shot from inside the bus looking forward at the moment of impact shows a wall of water fires up onto the windshield. This 'water barrel' technique is used to lessen damage and injury on many public roadways, and is used here to save the bus for use in another take - the one when it actually does hit the car a split-second of movie-time later. (01:42:15)
Continuity mistake: When Riggs and Murtaugh are driving to the house in Beverly Hills to shoot the guy in the pool, Riggs is lighting a cigarette and then Murtaugh says "You're not gonna smoke in the car." Riggs answers "Yes, but I'm gonna roll down the window." In the previous shot you can see that the window is already rolled down. (00:38:20)
Revealing mistake: Towards the end of the movie, watch the shots of the General in his car. Though he's supposedly speeding, the view we get through his rear windshield is of the ground going up and down, as if he was really just sitting in the car and pretending he was driving. (01:30:30)
Revealing mistake: In the wide shot of the bus colliding with General McAllister's car, look at the front seat of the bus and you can see that the driver is a mannequin.
Other mistake: Towards the end, when Riggs runs up to Murtaugh just after the car explodes, Riggs is carrying a large machine gun in his right hand. He runs up to the police barricade, but the police officer won't let him by until he shows him his ID. The police officer completely ignored the fact that Riggs was holding a large gun and could have been a criminal who wanted to use it.
Continuity mistake: Their car goes round the corner and the police light falls off the roof and dangles, yet is back on the roof a second later.