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)
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)
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)