Visible crew/equipment: When the car with Joshua in it is speeding away after shooting Riggs, you can see that he was the only one in the back seat. In the close up in the car, you can see the shadow of the camera and camera man play across his face.
Revealing mistake: As Joshua's chopper gets away, the camera follows it for a moment, then pans up to a long shot of the mansion. As it does so, the blades of the camera chopper can be seen at the top of the shot for a moment.
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.
Deliberate mistake: At the end of the film, two officers attempt to surround and handcuff Joshua. Using two officers to cuff someone is NEVER done for the exact reason of what ends up happening, as Joshua manages to grab a gun from one of the officers. Only one officer would have been doing the deed in the real world, but it's clear this error in being completely against police protocol had to happen so the good guys could prevail over the villain.
Other mistake: When Murtaugh hangs the target at the shooting-range the hole is already in the center.
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.
Factual error: Murtagh's picture shows him with a 173rd Airborne patch on his sleeve, and he later says his friend Hunsaker was wounded in 1965 in the Ia Drang in Vietnam. However, the 173rd Airborne was fighting at Bien Hoa at the time, which is hundreds of miles south of the Ia Drang. Although Murtagh may have been transferred before the picture was taken, it is highly unlikely that someone who "took a bayonet to the lung" would return to active duty so fast.
Revealing mistake: Early in the scene where the exchange for Murtaugh and his daughter is taking place in the desert, there are some aerial shots of a helicopter approaching the exchange site. The blades of the other helicopter, that is filming the aerial shot, can been seen at the top of the frame. (01:18:05)
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)
Plot hole: There is no way Riggs and Murtaugh would have let Joshua kill the two officers guarding the house, if they were already waiting for him. And if they didn't get to the house first, there certainly would not have been enough time for them to reach the house and leave a message waiting for Joshua in that short space of time. So, were they waiting for him or not, and why let two cops be killed if they were?
Suggested correction: They didn't get to the house before Joshua; they showed up after he killed the two police officers. The note is in a child's handwriting, so it's more likely that Murtaugh called the family to tell them to evacuate the house, and one of his kids left the note.
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.
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)
Revealing mistake: At the start of the movie where the nude woman jumps from her balcony, as she is falling and supposedly getting closer to the car, you can see after a couple of seconds, her body landing on the safety mattress thing, with a print on the top of it making it look like the street with parked cars. You can tell it is a mattress because just before they cut from the shot, the mattress dents inward. This could be taken for the top of the car denting in, except the dent "marks" extend from the sides of the roof of the car, into the bit of pavement beside the car. (00:04:05)
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)
