Factual error: In the desert shootout scene Murtagh throws what looks like an M67 "baseball" hand grenade on the ground. They wait for it to explode and Gary Busey says "it's a smoker". M8 smoke grenades look like a soda can, nothing like the baseball shape of a live M67.
Suggested correction: First, the grenade shown is more like the M61 "lemon" grenade. And there's no telling if Murtaugh/Riggs obtained a M61 based smoke grenade perhaps from a military surplus store that added the smoke effect for realism without the bang, or even a home made by Riggs grenade for this purpose, as opposed to using actual US Military M8 smoke grenades.
Factual error: When Riggs and Murtaugh are at the indoor shooting range, Riggs shoots a smiley face at long range. Every shot makes Mel Gibson blink and twitch from the bang. No expert marksman would react like that to the gunshot. Nor could his shot placement be so accurate with that reaction.
Factual error: After the car explosion in front of the Vogue theater on Hollywood Blvd, Murtaugh tells Riggs that "he's headed for the freeway" and "you can cut him off at the 3rd St bridge" (approximate wordage), and Riggs takes off running. 3rd St is nowhere near Hollywood Blvd (17 blocks away) and there is no 3rd St bridge within miles.
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.