Berating a gangster movie for being obsessed with style is a little like accusing a teenage girl of being preoccupied with her looks. Gangster pictures need to be stylish, and while we all know the law will have to win in the end, the good-guys-vs.-bad-guys showdown is only part of what we show up for: Faye Dunaway’s tilted beret and Robert De Niro’s slick three-piece suit, complete with glittering watch chain, are also part of the draw.

But Ruben Fleischer’s “Gangster Squad” has style to burn, and that’s the problem: It leaves behind nothing but ashy residue. In this semi-true story based on sort-of true events, Sean Penn plays Mickey Cohen, a gangster who’s angling to be the king of post-World War II Los Angeles. A stalwart Josh Brolin is Sgt. John O’Mara, the honest cop who’s been entrusted with the task of putting together a team to bring him down. That gang is played by a roster of performers including Robert Patrick, Anthony Mackie, Michael Peña and Giovanni Ribisi. But really, all eyes are on Ryan Gosling’s loner cop Sgt. Jerry Wooters, traipsing through the movie in a series of rakish fedoras as he woos – or would that be wooters? – Emma Stone’s saucy-hot Grace Faraday, who happens to be Mickey Cohen’s moll.

With a hummina-hummina pair like Stone and Gosling, “Gangster Squad” ought to sizzle. But there’s so much going on in the picture that they virtually get lost in it. Fleischer – who made a surefooted debut with the 2009 “Zombieland,” only to follow up with the wobbly 2011 “30 Minutes or Less” – appears to take great delight in the movie’s visual trappings, and some of them are shiny and distracting, all right. The movie’s production design, in particular – it’s by Maher Ahmad – gives us a late-‘40s Los Angeles that vibrates with neon; the city’s polychrome, manmade nighttime glow, as captured by cinematographer Dion Beebe, has a tawdry allure.

But Fleischer, working from a script by Will Beall (which in turn was adapted from Paul Lieberman’s book), doesn’t quite know how to put all the necessary parts together, particularly when it comes to the story’s violence. Early on, Cohen gives a visiting Chicago mobster a particularly grisly welcome; later, the contents of one character’s noggin get splattered on the far side of a dimpled glass door. Yet the violence is so indifferently presented that it has no kick; it’s not grim or graphic enough to shock, but it doesn’t rev us up, either. The picture’s various shoot-’em-up sequences are so generically conceived and shot that each one is indistinguishable from the next – by the movie’s end, they may as well all collapse into an exhausted heap.

The mere presence of Gosling and Stone offers occasional relief, although Gosling appears to be coasting a little too numbly through his performance. (His best moment: When he first eyes Grace at a nightclub and asks a buddy, with faux disinterest, “Who’s the tomato?”) Stone looks fabulous in an array of satiny cocktail dresses, but she’s way too foxy for this crowd – her dazzle makes everyone else in the cast look dim-bulb dull by comparison.

That’s especially true of Penn, who brings his pronounced oddball diction to lines like, “Roast peacock! The Romans couldn’t get enough of this stuff!” Penn could probably make a convincing gangster, if only he weren’t looking more and more like an apple doll -- “Granny Squad” is more like it. But who would buy a ticket to that?