Continuity mistake: At the shooting range, just after saying "That's very thin", Riggs has his arms outstretched, semi-aiming his gun. Cut to a two-shot, and he's got his arms into his body. (00:52:55)
Continuity mistake: As Murtaugh is interviewing Hunsacker, Riggs waits outside on the grass. At one point, the area Riggs is standing still in changes from full sun to full shadow in seconds. (01:13:15)
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)
Continuity mistake: The bad wound on Murtaugh's left shoulder (the one which got salted) disappears when he and Riggs drive back to his house. (01:32:35)
Revealing mistake: The hole in the windshield through which the General's driver was shot is not a hole but a round spot of cracked glass. Only before the car gets hit by the bus there is a shot of a hole big enough for a bullet to zip through. (01:30:20)
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)
Continuity mistake: When Riggs and Murtaugh kick Murtaugh's front door open they must have damaged the lock, but when the door falls closed the lock sounds as if it is perfectly OK. (01:09:15)
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)
Factual error: In the desert shootout scene Murtagh throws what looks like an M67 "baseball" hand grenade on the ground. They wait for it to explode and Gary Busey says "it's a smoker". M8 smoke grenades look like a soda can, nothing like the baseball shape of a live M67.
Suggested correction: First, the grenade shown is more like the M61 "lemon" grenade. And there's no telling if Murtaugh/Riggs obtained a M61 based smoke grenade perhaps from a military surplus store that added the smoke effect for realism without the bang, or even a home made by Riggs grenade for this purpose, as opposed to using actual US Military M8 smoke grenades.
Factual error: When Riggs and Murtaugh are at the indoor shooting range, Riggs shoots a smiley face at long range. Every shot makes Mel Gibson blink and twitch from the bang. No expert marksman would react like that to the gunshot. Nor could his shot placement be so accurate with that reaction.
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.
Revealing mistake: When the bus hits the car, the car launches into the air, propelled by a special-effects 'roll cannon'. The cylindrical slug that is fired out of the bottom of the car is seen rolling ahead of the bus toward the bottom of the screen. (01:42:15)
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: The kids in front of Dixie's house change positions between shots when they shout after Riggs and Murtaugh, like the one with the baseball cap who sits up. Furthermore, this little guy can't help glimpsing at the camera for a second. (00:55:40)
Continuity mistake: Shortly before the General's car gets hit by the bus the dead driver is leaning towards the side window. When the camera angle changes to inside the car his head is hanging forward. (01:30:30)
Continuity mistake: After Murtaugh shoots the General's driver the car is swerving around and the dead guy loses his sunglasses, but they jump back on his nose for the rest of the scene. (01:30:20)
Visible crew/equipment: When Riggs walks up to Dixie's house the camera is reflected in his sunglasses. (00:55:45)
Visible crew/equipment: When Riggs and Murtaugh compare their targets, a crew member sneaks up behind Riggs and disappears in the next shot. (00:53:30)
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.