Contested Sequel: Whilst the first two movies are by and large considered buddy-cop/action classics, 3 and 4 are much more divisive. To some they are installments that have reached the point of self-parody in terms of their level of goofiness with things like the continued presence and pushing into center stage of the Leo Getz character as well as not having as strong of scripts after the departure of Shane Black. Whilst to others they while not as good as the first two are solid entries that continue to show off the great chemistry between its leads, match if not up the ante in at least some of the action scenes, and rounds off the story-arcs of its characters well. Particularly Riggs who finishes his progression from a crazed suicidal man to a more down to earth and at peace guy who can move on with his life and allow himself to be happy.
Crazy Is Cool: Riggs "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.
In the first film, Riggs jokingly asks if the stock market crashed. Months after the film came out, Black Thursday happened.
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.
In the first film, one of the kids near Dixie's house says "My momma says policemen shoot black people!". It's a little more awkward these days, thanks to the high-profile police shooting of Michael Brown in 2014, spurring the emergence of the Black Lives Matter movement.
Part 3 opens with a terrorist blowing up a city building... as a punchline to a joke. Nine months later the World Trade Center was bombed, and the "joke" has only gotten less funny with each successive real-world incident.
Memetic Mutation: Danny Glover has always been, and will always be, getting too old for this shit. Also, if you made it through the early 90s without hearing people quote "They FUCK YOU at the drive-thru!" everywhere you went, you must have been in a coma.
My Real Daddy: Many fans and critics credit the series' quality and success to writer Shane Black. However, many of the series' signature elements, including the humor, were added by Jeffrey Boam in his uncredited rewrites to the first film and screenplays to the second and third. Black's original treatments were considerably Darker and Edgier than the final product, with the character of Riggs being an unstable psychopath killed off at the end of the second film.
Only the Creator Does It Right: Shane Black was only involved with the first two films. The first is considered a classic, while the second is widely considered the best of the sequels. The third and fourth films are somewhat divisive.
A not too drastic example, but most noticeable with part 4.
Shane Black disliked the sequels, as he felt they were too jokey and that they ruined the character of Riggs.
They Wasted a Perfectly Good Character: Plenty of fans liked the Mauve Shirt detectives from the second film (a colorful bunch played by some notable action movie actors) and would have liked to see them to play bigger roles in that movie or (if more than one of them had survived it) the franchise in general.