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.
Factual error: In the scene where Riggs and Murtaugh are in the police car, they intercept a transmission in Afrikaans for the first time in the movie. Except it's definitely not Afrikaans (my home language). I think it's Vlaams or Dutch.
Factual error: Nail guns like the one used as a weapon here can not be fired unless the tip is pressed against a hard surface. It will not fire a nail at someone across any space. The first guy is killed by pressing the gun to his forehead, but the second is hit from several inches away (evidenced by the length of each nail still sticking out of the guy instead of them being fully into his body with only the nail heads showing.
Factual error: The amount of money that leaves the cargo container when Riggs and Murtaugh use the car as a battering ram is nowhere near what was inside considering there were at least 4 or so pallets in front of the car. The car didn't have anywhere near the momentum to drive 'through' the pallets and leave them inside.
Factual error: In the scene where the car blasts out the container, the weight of those stacks of money would make it impossible, for a car parked so close to them, to blast them out the way like it does. There must be around 18 pallets of money stacked up on top of each other, even if they only weighed around 500kg each, that's 9000kg.
Factual error: When the guys arrive at the stilted home, a 'rollback' wrecker (flatbed tow truck) is shown with its bed raised and tilted to load car. At the higher, forward end of the bed is a massive 'guard' (shaped somewhat like a rollbar) that the warning lightbar is mounted on. This guard is specifically there to prevent a carried vehicle from being able to move forward past the front end of the bed. It is not possible for the car that is struck to go over the cab of the truck as it did, as this guard raises with the bed, and is reinforced to hold the car back, not breakaway in the flimsy fashion that it does. (00:37:20 - 00:42:35)
Factual error: Diplomatic immunity does not give a foreign diplomat carte blanche to openly and brazenly commit extreme crimes in their host country. Arjen Rudd and his men are known money launderers. Once Riggs begins harassing Rudd at the consulate, Rudd launches a violent campaign against the Los Angeles Police Department, assassinating half a dozen police officers. At the very least, the United States would be well within their rights to expel Rudd from the country and bar his re-entry. There is no way the South African government would oppose prosecution of Rudd given these circumstances, doing so would fracture all diplomatic relations with the United States. It is absurd for Rudd to shoot a cop and smugly proclaim "Diplomatic immunity!" after he has done so because it is not a "get out of jail free" card. If Rudd were expelled, he could face prosecution in his home country.