These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: Riggs tricking Murtaugh into taking his clothes off, running out into the street in just his boxers, socks and shoes, and dancing like a giant bird, supposedly to distract an arsonist with a flamethrower, and then admits he only suggested it to see if Murtaugh would actually do it, which leads to Murtaugh being humiliated for months. Also counts as Took a Level in Jerkass - he was never above pranking Murtaugh before but even for Riggs that was pretty low (and just makes it more awesome when Murtaugh punches him later in the film).
"You think I'm crazy? You think I'm crazy, I'll show you crazy!" *proceeds to slap himself in the face multiple times while wailing like Curly from The Three Stooges, pokes the drug dealer in the eyes, slaps the other drug dealers, and pulls out a gun.
"Funny Aneurysm" Moment: Riggs mocks Rudd's racism and calls him "Aryan" in the second film. Cut to 2006, and Mel Gibson is in hot water for making several racist remarks during his arrest. Cut to 2010, and he's in even more hot water for making even more racist statements during an argument with his girlfriend.
Sequelitis: A not too drastic example, but most noticeable with part 4.
Values Dissonance: On two separate occasions in the first film, Riggs demonstrates extreme homophobia. Perhaps fair for its time in 1987; stands out quite a bit in 2011.
Villain Sue: Jet Li's character descends into this with some of his more outlandish feats, in Mexican Standoff, he takes dismantles Riggs' gun with 'one deft move', and in another, he easily kills a man by grabbing his neck.
Backfires on him when he performs an impossible Bullet Dodge...And the round hits his brother instead, killing him.