Continuity mistake: At the end of the movie, when Riggs is in the cargo area, a gunman shoots at him, he rolls and starts emptying the clip into him - you see the bullet holes in the gunman. But as Riggs is face to face with the gunman, the holes disappear.
Continuity mistake: While he's on the toilet, Murtaugh is wearing a flak jacket that disappears for one shot while he is getting instructions from the bomb squad leader.
Visible crew/equipment: When Riggs first starts shadowing Rudd, he cuts off Rudd's car with his truck. They go to the close up shot of Riggs and when he drives away you can see in the reflection of the trucks window, the PANAV on the hood of the Panavision camera.
Deliberate mistake: The way diplomatic immunity is depicted in the movie is extremely inaccurate. While technically a sufficiently ranking diplomat could perform the acts shown in the movie without being subject to arrest, their home government would be requested to turn the diplomats over for trial, or the diplomat would be declared persona non grata and expelled from the country. A drug smuggling ring and murdering multiple policemen is far, far more serious than actual crimes that diplomats have been expelled (or handed over for trial) for in the real world. Additionally, the consul general and his officers would not be considered diplomats. They would only have limited consular immunity with regards to "official acts" in the course of consular business.
Factual error: All vehicles sold in the U.S. since the 1950s have federally-mandated laminated windshields. When the surfboard crashes through the windshield of the truck, the windshield shatters like ordinary unlaminated glass.
Audio problem: In the scene where Leo explains how he launders the drug money and Roger says "You're a cheat", Leo says "Come on, everyone cheats a little, look at the pentagon." But when he says "look at the pentagon", it's dubbed in because the sound of his voice doesn't match his other dialogue, and if you read his lips it doesn't match either.
Continuity mistake: The right headlight of Murtaugh's car, when it is chasing the BMW, falls off when he hits something, but later on it is fine.
Continuity mistake: In the fight scene toward the end of the film between Riggs and the guy who killed his wife and Rika, look carefully at the watch Riggs is wearing - it moves from one arm to the other in close-up as Riggs forces the guy to stab himself.
Continuity mistake: During a chase scene involving Murtaugh's station wagon and a flatbed tow truck, the hotel waiter shoots at Riggs through the truck's rear window. In this series of shots, notice how Riggs is swinging by a chrome handle on the passenger's side - which wasn't there during the gunpoint hijack shot just moments ago.
Continuity mistake: After Murtaugh confirms the Alba Varden is a ship, one of Rudd's henchmen enters the house armed with a knife. Moments later when they're struggling by the hobby room's blueprint table, Murtaugh grabs the nail gun and shoots him in the forehead. Now right here, you can notice the sound of a knife being thrown to the floor as he reaches for his head. But when the henchman is up against the unhinged doors, he's once again holding a knife in his right hand.