Continuity mistake: When Murtaugh starts questioning Alfred about the suspicious man he saw near Dixie's house, Alfred lifts up his sunglasses. Through a few questions, the glasses' ear stem rests normally behind his ear where it should (left one is visible). Suddenly Murtaugh asks about the man's hair color, but now the ear stem is hanging off. (01:09:40)
Continuity mistake: When Riggs is out one night trying to locate Dixie the streetwalker, he shows her photo to strangers. But if you look, the photo is of an Asian woman. Bears no resemblance to the real Dixie we saw in an earlier scene. (00:09:45 - 01:08:20)
Continuity mistake: The pattern of scars on Riggs' face changes when he comes to deliver his bullet to Murtaugh: The two cuts on his left cheek become three, and the lesions on his chin disappear. (01:39:40)
Continuity mistake: During the staged drug deal the items on the table move around. Check for example the little bag with the sample and the can in front of Riggs when he takes his wallet out. (00:11:30)
Continuity mistake: The lawn in front of Dixie's house turns completely into naked dry soil at the end of the scene, even at places where it should not be really affected by the extinguishing operations. (00:57:25)
Answer: The jumper's name was Len McCleary. He was played by Michael Shaner and is credited for the role in the film (and on IMDB).
Bishop73