Continuity mistake: During the car chase involving the car driven by the Chinese guy, Murtaugh, and the mobile home, the two cars slide against each other and the right wing mirror on Murtaugh's car is completely wrecked. Once the two cars are separated the wing mirror has miraculously repaired itself. The left wing mirror also does a disappearing / reappearing trick.
Continuity mistake: In the scene near the end of the film when Murtaugh shoots at Wah Sing Ku and mistakenly kills the last of the four fathers, you can clearly hear an empty shell casing hit the floor, although he is using a revolver, which do not spit out the empty shells as they are fired.
Continuity mistake: At the end of the movie when Riggs, Murtaugh and the other two cops enter the garage where the Triad chief is buying the four fathers' freedom whe can clearly hear the hard rain outside, but the car that they're driving is completely dry - maybe they had a very big umbrella!
Continuity mistake: During the gunfight with the armored man, more and more bullet holes continue to appear on Riggs and Murtaugh's side of the car which is facing away from the armored man with the gun. And in one brief scene from the armored mans view, there are no bullet holes on the side of the car which he had fired at and hit several times.
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.