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: 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: Near the beginning, when the tanker trailer is blown, you can see where each of the charges are placed the moment it blows as well as see the rear wheel of the tanker mechanically fold under.
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.XIII
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.
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: 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.