I like the hard-to-solve mystery we get here. Actually, they don't even come close to giving us enough clues to solve it, hence the difficulty. But in that we feel we're up against it like the protagonist, detective Phil Marlowe, played by Elliot Gould.
Times have really changed for Marlowe since 1946, when he was played by Humphrey Bogart. Then he was cool, implacable, wore a fedora a lot, and wound up with babe Lauren Bacall. That was the only strain of the plot viewers could follow. There were some dead bodies, smoking guns, and tough questions from cops along the way.
In this movie it's 1973, and Marlowe still think he's cool but that opinion is not so widespread this time - he's being played for a sucker by at least half the cast, including a longtime friend, and his own cat. He unravels the mystery mostly out of a lack of having anything better to do, which he clearly stood in need of.
Director Robert Altman follows his own ideas about how to communicate visually. Like when he changes scene to a hospital, he doesn't do any kind of establishing long shot, he shows a closeup of a light over a patient's bed. His montages create a kind of equivalent of our human experience, where we use our minds to focus on detail. He usually winds up with scenes that feel like we're watching something actually happen. But he does know how to use visuals for dramatic power when he wants, as the ending makes clear.
Some of the performances he gets from actors are amazing, like Mark Rydell as psychotically dangerous gangster Marty Augustine. The way he works himself into a rage with his rants changes gears from funny to frightening at high speed, and I can't believe it didn't influence Joe Pesci's performance in "Goodfellas."
Not everything works here, like Gould smearing fingerprint ink on his face then breaking into Al Jolson at police headquarters, but on the whole a fairly engrossing take on detective mysteries.