Continuity mistake: The kids in front of Dixie's house change positions between shots when they shout after Riggs and Murtaugh, like the one with the baseball cap who sits up. Furthermore, this little guy can't help glimpsing at the camera for a second. (00:55:40)
Continuity mistake: Shortly before the General's car gets hit by the bus the dead driver is leaning towards the side window. When the camera angle changes to inside the car his head is hanging forward. (01:30:30)
Continuity mistake: After Murtaugh shoots the General's driver the car is swerving around and the dead guy loses his sunglasses, but they jump back on his nose for the rest of the scene. (01:30:20)
Continuity mistake: Their car goes round the corner and the police light falls off the roof and dangles, yet is back on the roof a second later.
Continuity mistake: When Murtaugh meets the General's people in the desert the door of his car gets blown open by the helicopter. When he pulls out the grenade the door is almost closed again. (01:16:10)
Continuity mistake: When Murtaugh steals some bacon from the tray there is about twice as much than in the shot before. (00:07:20)
Continuity mistake: When Murtaugh drops Riggs off in the desert it's sunset, but when we see the car in the next shot the sun is way up again. (01:12:55)
Continuity mistake: When Riggs talks to the jumper his hair is either fluffy or stabilized with gel, depending on the camera angle. (00:30:00)
Continuity mistake: Towards the end before Riggs saves Roger and his daughter he is wet, but when he is running on the street his hair is absolutely dry.
Continuity mistake: When Murtaugh comes downstairs and checks his tie it's on the outside of his vest. He then walks through a door and the tie is on the inside of his vest.
Continuity mistake: After the car crashes into Murtaugh's living room, Riggs escorts Joshua out onto the lawn. As Murtaugh starts patting him down, a shot from behind shows Joshua with his hands behind his head. In the very next shot from the front, his hands are now lower, behind his neck.
Continuity mistake: When Riggs is counting out of the money to pay the three drug dealers, he puts a 20 dollar note on the table. The wind then blows the note against the bag of cocaine and it is lying flat down, but in the next shot the note is folded up.
Continuity mistake: When Hunsaker is talking to Murtaugh in his house, the shadows outside dramatically change throughout the scene. First the sun is beating down on Riggs from the right (over the ocean), then from the left leaving Riggs under a bunch of shadows from the tree. This constantly changes throughout the scene.
Continuity mistake: In the scene following Riggs and Murtaugh's conversation on Murtaugh's boat, Riggs crumples a beer can, and Murtaugh holds open the trash can lid, but the can falling into the trash can is intact, not crushed.
Continuity mistake: When the helicopter with Joshua comes up and he starts firing at the house, Hunsaker has both hands on the carton of eggnog. When the camera cuts to a wide shot, he's starting to react to being shot again, and his left hand is about a foot away from the carton.
Continuity mistake: Riggs is completely dry before he begins his showdown with Mr. Joshua, but after Mr. Joshua says "Don't mind if I do", we cut to Riggs, and he is now soaking wet.
Continuity mistake: When Riggs is fighting Mr. Joshua at Murtaugh's home towards the end of the film, the lawn is completely saturated in water from the spray at one point, but in the next shot appears completely dry.
Continuity mistake: After Joshua is leaving Hunsaker's home after killing him, he is talking to Peter on a mobile phone and it is nearly dark. In Peter's scene in the car, the sun is still up and it is late afternoon/early evening. They are both in the same city.
Continuity mistake: When Riggs is working undercover at a Christmas tree lot sampling cocaine, he agrees to do business with the dealers. After one of them quotes a price, Riggs sits there looking pleasantly surprised. At this point, note how the sky behind his right shoulder is mostly overcast. Seconds later, Riggs shakes his head in agreement and reaches for his wallet - but by now mostly all of the cloud cover has vanished (as if minutes have passed by). (00:17:10)
Continuity mistake: On the shooting range, Roger hangs the target on the mechanical arm and runs it out a short distance. After it settles, the bottom hangs at about ten° to the left of the target's center. After running it back to show to his partner, and before Riggs runs it all the way to the wall, the bottom now hangs about 3 to 5° to the right of the target's center.
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