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The Yakuza is not a lost classic of '70s cinema. Robert Towne was paid an awful lot for the script, which does do a nice job of using noir tropes as setups for chop-socky fight scenes, but it's lumpily-paced and frequently confusing, with hunks of exposition so ungainly that Lumet has no choice but to fade and dissolve his way through the speeches..
It's always fun to watch Robert Mitchum wisecrack with the guys and pine for the girl, and paunchy, puffy 70s Mitchum is just as much the ideal man than the young, beautiful Robert Mitchum---maybe more so. He and the able, charismatic Ken Takakura seem like they could get a really good rhythm going were Takakura not so visibly derailed by the English language---when acting in Japanese, he's as quick and smooth as in the fight scenes, but every time he has to speak English he drops his arms to his sides and twists his head like he's frozen at a desk. Their climactic fight scene, when they jointly kill several score bad guys, armed with Takaura's sword and Mitchum's Halo-like pistol & shotgun combo, is their one chance to get a good non-verbal relationship to happen, and it's squandered by the back-and-forth editing and uncreative framing.
But even though Pollack's visual direction is stolid, the visuals are still pretty thrilling, thanks in large part to Stephen Grimes' endlessly groovy production design. Grimes has a star-studded production design career, and he sinks his teeth into the scripts opportunities for campy japonaiserie, including a bright-blue boss' office with surrealist decor, and a sauna with inexplicable high-contrast red floor, equally inexplicable aquarium and even more inexplicable Porkysesque window to the girl's locker room. He has a great time filling the frame with artful patterns, or just a whole lotta brightly-colored Asiatic stuff, as well as finding some terrific city-of-the-future locations.
Director of Photography Kozo Okazaki also does a lot to keep the visuals exciting too, with great use of good ol' 70's Technicolor. The variety of rich, stylized hues are enough to make you weep for the candy colors that were to take over Hollywood filmmaking. I'll admit, this may be entirely personal, as despite being a child of the 80s, I feel that way about most films made between about 1968 and 1981---even the worst have a look that feels real in a way almost no color film would again, which may be one of the reasons 70s horror, no matter how crappily-made, has as unnerving authenticity.
Lumet's actual direction is really just workmanlike, with enough pans, dollies, and fades to feel properly professional, but most of the real visual magic is being worked by the production team. This is one of the nice things about having a full-crew sense of who makes a movie---even when the movie isn't much as a whole, there's still plenty of fine workmanship to admire, as well as some bizarre costume choices to, er, enjoy.