Continuity mistake: When Riggs is hanging off the roof and the others are trying to move a dumpster for him to drop into, the handcuffed Chinese waiter is trying to help. A shot from the top shows the waiter pushing the dumpster with his (outstretched) leg, but a split second later, a shot from the side, he has his back to the dumpster.
Revealing mistake: When Riggs jumps from the car onto the house that's being moved, you can see when the stuntman replaces Mel Gibson. Look at his hair, it changes styles as he jumps.
Continuity mistake: The scene on the highway where Riggs and Murtaugh are chasing the black Mercedes in their Pontiac, the windows on the Mercedes repeatedly change between tinted and non-tinted.
Continuity mistake: During the mobile home chase, you can see a white car following Murtaugh. In the next shot, when he starts to overtake the mobile home, the car is black.
Deliberate mistake: When Riggs is chasing the guy on foot, you can clearly see it is a stunt double, who is also very apparent in other shots throughout the film.
Factual error: Early in the film, while Riggs, Roger and Leo are on the Code 7, Riggs has to place his Beretta in his mouth so he can board the larger ship. The Beretta 92FS is a heavy handgun, it would be very difficult, if not impossible, for it to be held in the mouth, let alone to wave your head about like in the film. I own a Beretta 92 and I've tried it, so I'm speaking from experience.
Plot hole: When Riggs, Murtaugh, Lorna and the others are tied up and lying on the floor of the burning house, they can't stop coughing. However, the bad guys (who are also in the burning house) are just standing around laughing, wouldn't you think that they would be inhaling smoke also?
Continuity mistake: In the trailer chase scene, when Riggs is being dragged by the plastic wrap, it cuts away to a far shot of Riggs on the table. The "plastic" he is holding on to is very obviously a thick metal cable wrapped in saran wrap or something to make it look like plastic.
Continuity mistake: When Riggs, Murtaugh and Butters go to see Uncle Benny, Riggs sits down on Benny's desk with Butters to the left of him. When Riggs says flied lice, he's on the other side, sitting at an opposite angle, just as if the shot was flipped.
Factual error: Riggs shoots Ku to death with the AK-47 underwater. Guns can fire underwater, but the bullet loses most of its killing velocity. This would have been unable to kill Ku.
Suggested correction: If Wah Sing Ku was far away, this would be true. But Riggs is shooting with the barrel pressed directly against Wah's chest. It's definitely lethal at that range.
Revealing mistake: During the car chase when the Pontiac is about to jump into the office building, you can see a white stunt driver from the left side mirror, though Murtaugh is driving.
Other mistake: When Riggs and Murtaugh are assigned as new captains, they throw their old badges to the Chief and he catches them in his left hand as he grabs the new badges out of the desk draw with his right. In the next shot where he passes them the new badges, he is not shown to have swapped the badges over, so essentially he passed the old ones back to them.
Revealing mistake: In the scene where Riggs and Murtaugh's vehicle breaks through the glass to get back on highway, the vehicle sparks even before it hits the pavement.
Continuity mistake: In the scene where Riggs is at his wife's grave, Leo comes along to give him advice. In the scene he was in previously he had cuts across his face. At the cemetery the cuts are gone, then they reappear in the following scene at the hospital.
