Continuity mistake: When Rika comes to Riggs' trailer he offers her a chair, and she sits down twice in different camera angles. (01:07:50)
Suggested correction: This is too subtle to be called a mistake - she's in the process of sitting when she's facing the camera, the shot changes to behind her and she's seen finishing her settling into the chair - this could just as well be her making a natural adjustment to her sitting position. It's not an obvious mistake by any means.
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.
Continuity mistake: When the boss gives Riggs and Murtaugh the Leo assignment the name on the office door changes from Capt. E. Murphy to Capt. L. Murphy when they leave the office. (00:24:30)
Continuity mistake: Murtagh states he was 7 floors up, but the room number (612) suggests it's a 6th floor room. When he looks down to see the three men falling, his vantage point is well above 7 floors up. (00:30:20)
Plot hole: The hitman in the tow truck leans into the rear/left corner of the cab as the surfboard approaches. The board hits the glass at the very top, dead center. Hence, it definitely misses him completely, yet the hitman is killed. Windshields don't break into "shards" (which is another mistake made listed here, and as it can't exist, it can't be the cause of death) and the roof is not damaged. He is the driver, and he stops the truck by braking. There is no vehicle collision. It is clear to all viewers that the makers intended the surfboard to be the cause of death - nobody watching the film thought otherwise.
Character mistake: The sign Riggs holds outside the South African Embassy has a spelling mistake. The sign says "end apartheid now" but the word apartheid is misspelt as "aparthied".
Plot hole: Riggs and Murtagh send the car flying out of the container, pushing the money out as it goes. Ignoring that the car couldn't possibly force the sealed container doors open, even without having the obstacle of pallets loaded with money in the way, the car actually explodes in mid air for no reason. (Director's Cut.) (01:44:35)
Revealing mistake: Movie physics occasionally dictate random explosions, but this is too bizarre. Near the start, a cop car smashes through a caravan, and the caravan blows up. Fair enough, may have hit a gas cylinder or whatever. We see the cop car, practically undamaged, skid to a halt. Cut to a few reaction shots, then suddenly the cop car just blows up for absolutely no reason whatsoever. (00:02:25)
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: When Riggs and Murtaugh make the car go through the container door it has only a few meters to accelerate. It would have never been able to gain enough speed to leave the container almost horizontally. (01:36:15)
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.
Visible crew/equipment: When Riggs is thrown off the tow truck and rolls across the ground a camera peeks in from the right. (00:37:25)
Revealing mistake: When Riggs and Rika make love a safety blanket separates the crucial areas. (01:16:25)
Continuity mistake: In the scene where Murtaugh is shooting his attackers with the nail gun the walls are apparently covered with super plastic. How is it that the plastic sheeting is light enough for the bad guy to punch through, but is able to support the weight of his corpse by a single nail when Murtaugh shoots him through the plastic? Wouldn't the plastic tear and drop the body to the floor? (01:15:45)
Continuity mistake: In Lethal Weapon 1 Murtaugh turns 50. In Lethal Weapon 2, you can see a copy of Murtaugh's police file in the South African Embassy, when they are discussing repercussions against the police. In the file it says Murtaugh was born in 1947 which would make him 42 in this movie.
Continuity mistake: Near the end, when Riggs is captured by the bad guys they tie him in a straight-jacket and toss him off a pier into the drink, he's wearing a pair of Dingo style boots. Underwater when he dislocates his shoulder and escapes the straight-jacket, he sees Patsy Kendit's corpse, swims over, checks her pulse and swims to the surface. Now he's barefoot. Yet when he attacks and kills the two thugs he's got the boots on again. They can even be heard on the pavement.
Revealing mistake: When the small car is launched into the air, the underside is plainly visible, showing no normal working parts like a suspension or drivetrain. It has a flat pan bottom with a square-tube support structure to make it very light for its flight and to retain it shape. (Director's Cut.) (00:42:40)
Deliberate mistake: It's surely an intended joke, but that the toilet not only survived the explosion but also the landing in one piece is very unrealistic. (00:57:15)
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: 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.