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.
Plot hole: In the opening chase scenes, the bad guys are using hand-held radios to communicate, and several shots show that all the police are hearing them. These professional criminals would not be broadcasting their criminal activities on a police frequency, nor are the police and their dispatchers monitoring scanners to pick up the criminals' frequency. So neither side should be hearing the other. (00:01:50)
Continuity mistake: After leaving the Embassy, when Murtaugh pulls over after Leo says there's a deli, he parks in front of a white car and is near a bush and some grass on the ground. From inside the car, the white car is no longer present and when the door is ripped off, they are now parked in a different spot, no bush or grass is around.
Continuity mistake: When Pieter throws a knife at Riggs from offscreen, it sticks into his leg. Note that most of the blade is still visible. All things considered, the knife could have been able to penetrate maybe two, three inches into the skin (at best). But look closely in the following shot as well as subsequent shots where Pieter starts kicking Riggs in the face and you'll notice how the knife has managed to drive itself completely through and out the opposite side. Arguably the knife could be long enough and, with immense effort, this might be possible, but Pieter throwing a knife all the way through Riggs' thigh just seems absurd. (01:46:45)
Continuity mistake: When Riggs jumps from Murtaugh's station wagon to catch up with the BMW on foot, he springs onto its rear window and asks the driver for proof of insurance. Interior brake lights are shining on his clothes before he falls to the pavement. Seconds later the driver stops to take a shot at Riggs, but now the BMW is missing the interior brake light altogether. (00:03:40)
Continuity mistake: After Riggs' Houdini-esque underwater escape, he makes his way to the pair of hitmen on the docks above. One of them gets thrown through a car door's glass window, and Riggs uses that same door to bash his head repeatedly. As Riggs is dealing the blows, pay attention during the close-up shots and you'll see reflections in a brand new piece of glass. (01:32:50)
Continuity mistake: After inviting Rika to his trailer, Riggs walks inside and opens his fridge to get a beer. On top of the TV nearby is a VCR. Flash forward to the helicopter attack scene where Rika and Riggs are about to escape through Sam's doggy door. Here you can see there's no longer any VCR on the TV set. (01:14:20 - 01:24:15)
Continuity mistake: When the hotel waiter shoots at Riggs through the flatbed tow truck's rear window, Riggs manages to cling to a handle on the passenger's side and avoid being hit. However, immediately before the waiter runs out of bullets and throws down his gun, look sharp and you'll see how all of the window's busted glass is once again intact, like new. (00:40:50)
Visible crew/equipment: When Riggs turns up at the house as the pool cleaner you can see the reflection of the camera crew in the window as he walks along the balcony.
Visible crew/equipment: When they fall out of the hotel and into the pool the side shot shows two dark things under the water - this is the under water crew filming the close ups of the actors. The crew cannot be seen in any other scenes around the pool, only on the entry scene.
Continuity mistake: At the end when the shootout on the Alba Varden has finished, as police cars are shown driving over the bridge while Murtaugh attends to the wounded Riggs in the cargo area, the sky is pitch dark. Two minutes later when the credits are rolling, the sky is now much lighter. (01:46:40 - 01:49:00)
Other mistake: During the "high speed chase," Murtaugh stops the car so that Leo can retrieve Riggs' dropped gun from the side of the road. He picks it up and runs back to the car. Murtaugh says, "Give me that," and takes the gun from Leo. But, Murtaugh, being in the driver's seat, wouldn't be able to reach over the passenger seat and a foot or so outside of the car to grab the gun from Leo. It looks like someone in the passenger's seat just reached out and grabbed it.
Continuity mistake: After Riggs uses his truck to pull down part of the house on stilts, the tow cable on the back of his truck disappears as he drives away while the house is falling.