Yeah, that's not a very exciting title, but I recently rewatched L.A. Confidential and it struck me as being a very smart and well-done screenplay which nicely surmounts the difficulties of multi-protagonist movies. Here's how:
1) The period voice-over --> character switcheroo: the movie tells us all we need to know about the set-up through a voice-over over period media. We get glamour and crime photos and movies, intermixed with some regular film detailing the fall of L.A.'s crime kingpin and the vacuum that's created. But even better, rather than just serve as background, we learn that this voice-over is from Danny Devito's sleazy tabloid journalist who will feature later in the story. That's our first character introduction and also our setting introduction--two for the price of one.
2) Short, pointed introductions to the multiple characters:
Bud White (Russell Crowe) hates wife-beaters, will tell us why in very simple terms later: our intro to Bud is a close-up of his impassive face as he listens to a domestic dispute, which leads, of course, to his calm demeanor as he beats up the wife-beater. Extra points for having him lift up a wire so the wife can go under it and respond unironically, "Merry Christmas, ma'am." That's all we need to know about him: he's a simple guy who wants to protect women. (Later, he will retell his Freudian childhood of watching his dad beat up his mom. The dad gets away, which will come up later.)
Jack Vincennes (Kevin Spacey) is a sleazy Hollywood cop: Jack V. is a technical advisor for the show Badge of Honor and an associate of Danny Devito's sleazy tabloid journalist. Like Bud White, Jack only cares about results, though his results are all self-glorifying.
Ed Exley (Guy Pearce) is a goody-two-shoes with a heart of brass: All the other cops are getting drunk but Ed is on duty. He's also introduced in a close-up of worried/impassive face, but this time he's watching the cops get drunk. We also hear here that he's trying to live up to his dad, so we've got that motivation. But pretty soon, after all the cops go to attack some cop-beaters, Ed turns against the force in order to rise within it--because he's all about moving up in the world, even though he won't play the games the other cops play. (Later we'll learn that Ed's dad died and the cops never avenged him. So both Bud and Ed are on the same quest: vengeance in the name of Dad. And as we'll see, James Cromwell's Dudley Smith is pretty dad-like.)
In all of these case, the characters may grow or become more complex, but the introductions are quick and to the point.
3) Not just plot relation, but thematic relation: there's all the dad stuff lurking below the surface of this movie for the two main characters, Ed and Bud, who both got into this job because of dad. Jack V. is less clear as a character, though that itself is played for meaning: after Bud and Ed describe their reasons, Jack confesses that he no longer knows why he became a cop. If the others are son in search of a dad, Jack is a boozy dad who feels like he's betrayed his son.