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: When Clay, Julian, and Blair are driving from Palm Springs to Los Angeles almost at the last scene, Julian dies as they are driving through Joshua tree. That would be the opposite direction to travel from Palm Springs to Los Angeles.