Revealing mistake: Riggs handcuffs himself to the depressed businessman. They jump off the building but they're not handcuffed to each other anymore. They used plastic cuffs which could separate during the stunt in case anything went wrong. They break just as they jump, so they grab each other's hands to stay in contact. After they land the cuffs are attached again.
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.
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.
Revealing mistake: In one of the first scenes of the movie you see Riggs in his trailer. He walks out of bed smoking a cigarette and taking a beer. When he takes his first drink of the beer some fluid is spilled. If you look at it, it is not beer. It's probably water, but definitely not beer.
Revealing mistake: Early in the scene where the exchange for Murtaugh and his daughter is taking place in the desert, there are some aerial shots of a helicopter approaching the exchange site. The blades of the other helicopter, that is filming the aerial shot, can been seen at the top of the frame.
Revealing mistake: At the start of the movie where the nude woman jumps from her balcony, as she is falling and supposedly getting closer to the car, you can see after a couple of seconds, her body landing on the safety mattress thing, with a print on the top of it making it look like the street with parked cars. You can tell it is a mattress because just before they cut from the shot, the mattress dents inward. This could be taken for the top of the car denting in, except the dent "marks" extend from the sides of the roof of the car, into the bit of pavement beside the car.