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.
Continuity mistake: In the scene where the girl jumps to her death from the balcony, it shows her hitting the car towards the right halfway onto the windshield. Then in the next shot, it shows her laying right in the middle of the roof of the car.
Continuity mistake: When Mel Gibson is talking about the special bullet, kept as the suicide special, he describes it as a hollow point - to do the job right. When he shows the bullet it is a full metal jacket.
Visible crew/equipment: When the car crashes into the bus and lands on its top, you can see a big square hole cut out of the car's underside.
Continuity mistake: At the end, when Riggs is at his wifes grave, it's supposedly raining. In one shot you see Riggs' hair is dripping wet, and when you see him bend down to put the flowers on the grave in the next shot, his hair is dry, and in the next shot it's wet again.
Continuity mistake: During the scene where the General is escaping in the car and Murtaugh shoots the driver. When the car is hit by the bus on the avenue you can see part of the device that makes the car flip over and roll away from the crash.
Continuity mistake: There is a scene where Riggs and Murtaugh are driving in a car, and the column shifter keeps going from park to drive and back.
Continuity mistake: When Hunsaker's shot, his eggnog gets all over his tie and shirt. When the camera angle cuts to Murtaugh's reaction, Hunsaker's shirt and tie are clean and there is no eggnog pouring from the container. Also there is no hole of any kind in the glass door behind him in which the bullet made.
Continuity mistake: In the scene where "the General" and his driver were fleeing down the alley, the driver is shot. The general takes control of the wheel and carries on driving, but the car is in park...
Continuity mistake: The Christmas illumination on the balcony of Amanda Hunsaker's hotel room is arranged in three different ways: In the first shot, before she takes drugs, it is attached to the side of the railing. When she steps out, the lights are hanging about 10 inches below the railing, like they are later when Murtaugh searches her room. And when she climbs up to jump the bulbs are directly hanging down from the railing.
Continuity mistake: As Riggs exits the car, he takes the cigarette out of his mouth. The camera angle chages to show him standing outside the car, handling his pistol, and the cigarette is back in his mouth, with no time to put it there and the audio indicates the shots are consecutive time.
Continuity mistake: In the scene where Riggs is chasing Joshua and is told by Murtagh to take a shortcut to catch Joshua, he is shown running in bare feet. After shooting at Joshua from on top of the freeway he then runs down the embankment and is shown wearing tennis shoes, but there is nowhere these shoes could have come from and he is never shown putting them on.