The first time we see Riggs in his trailer, there's an advert for some new aftershave called "Hero" on the TV. During the attack on his trailer later, there's a close-up shot of a bottle of aftershave being destroyed - freeze-frame it and you'll see the brand: "Hero" again. See more...
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Plot hole: During Riggs' last fight with Adolph, Adolph holds the knife in his own hand as Riggs forces him to stab himself very slowly. At any point, Adolph could simply have let the knife fall or just tilt down before that happened. Nothing Riggs is doing is making such impossible. "Locking" his wrist does not prevent him from letting go of the knife. It only prevents him flexing his wrist. And this guy is a trained killer, fighting for his life. Better to battle for control of the knife than just let it kill you.
Revealing: The building used for the South African Consulate is actually a bank. When Roger and Leo are thrown out, the glass front doors are marked with winged logos and consulate lettering that is dark in color, but one door has additional white lettering that says "Open to Serve You, Monday - Thursday 9am-4pm, Friday 9am - 6pm"- rather out of character for a consulate.
Deliberate "mistake": The way diplomatic immunity is depicted in the movie is extremely inaccurate. While technically a sufficiently ranking diplomat could perform the acts shown in the movie without being subject to arrest, their home government would be requested to turn the diplomats over for trial, or the diplomat would be declared persona non grata and expelled from the country. A drug smuggling ring and murdering multiple policemen is far, far more serious than actual crimes that diplomats have been expelled (or handed over for trial) for in the real world.
Factual error: The amount of money that leaves the cargo container when Riggs and Murtaugh use the car as a battering ram is nowhere near what was inside considering there were at least 4 or so pallets in front of the car. The car didn't have anywhere near the momentum to drive 'through' the pallets and leave them inside.
Continuity: When Hans first walks into the room with the fishtank, the plastic on the floor flaps up behind him as he walks, ending up folded up on itself without much space between the man and the end of the plastic. When he gets shot and falls back onto it, it's perfectly flat and he's a lot further forward.