If the slick and silly “Leatherheads” is any indication, the time George Clooney spent with the Coen brothers has rubbed off on him. Clooney’s third stint in the director’s chair is a loopy Roaring Twenties screwball comedy, and much of its wry, slightly detached humor is reminiscent of the Coens’ Clooney-centric “O Brother, Where Art Thou?” and “Intolerable Cruelty.” It feels a bit “Raising Arizona,” too, which starred Nicolas Cage but could have just as easily starred Clooney.

An even greater influence, of course, are the dialogue-heavy comedies of the 1930s, and Clooney breezes through “Leatherheads” — both as director and star — with the confidence of a man who knows the style forward and backward. When his character, an aging but still footloose playboy, quips, “You’re only as young as the women you feel,” you can imagine it coming from the mouth of Clark Gable or Cary Grant. Or, for that matter, from the real-life Clooney.

The film is set in 1925, at a time when college football is well funded and respected while professional football is a chaotic joke played by unsportsmanlike ruffians. Dodge Connelly (Clooney) is the captain of the Duluth (Minn.) Bulldogs, a pro team that’s on the verge of closing up shop until Dodge gets the bright idea of hiring college golden boy Carter Rutherford (John Krasinski). Carter, fresh-faced and all-American, brings legions of fans with him, thanks not just to his gridiron prowess but to his status as a hero of the Great War, in which it is said he once captured a trench full of Germans single-handedly.

The Bulldogs’ fortunes change overnight. Suddenly the stands are full of spectators, and suddenly the team is occasionally even winning a game or two. There is also new media scrutiny, in the form of Lexie Littleton (Renee Zellweger), a Chicago Tribune reporter who’s been assigned to get the real dirt on Carter’s war heroics. She travels with the team, cozies up to Carter, and butts heads with Dodge in that old Grant-and-Hepburn fashion. Their repartee (originally penned by sports writers Duncan Brantley and Rick Reilly, though Clooney gave the script a major overhaul) is saucy and cute, genuinely recalling the 1930s comedies that it’s meant to evoke, and Zellweger is as adept at playing old-Hollywood characters as Clooney is. (Krasinski, on the other hand, always seems too modern for the film, though his performance is otherwise keen.)

The film’s midsection sags a bit as two plot threads jostle each other for attention. One deals with the Carter-Lexie-Dodge romantic triangle; the other centers on Carter’s war record and his and Lexie’s ever-shifting views on whether to go public with the truth. (Suffice it to say he didn’t exactly capture all those Germans single-handedly. The real story, seen in flashback, is much funnier.) Both facets of the plot are important; they just need to be juggled more elegantly, maybe with a little tighter editing and sharper focus.

Clooney’s grinning, Clark Gable-y insouciance eventually sets the tone for the entire film, with everyone calibrating their own performances to match his. That includes Stephen Root as a consistently inebriated sports writer (is there any other kind?) who usually just prints whatever Dodge dictates to him, and Jonathan Pryce as a conniving sports agent (is there any other kind?) trying to make a buck off of Carter Rutherford. Even Randy Newman’s old-timey musical score feels jaunty and carefree, a perfect match for the goofy merriment of the story. Many people already consider Clooney to be the 21st century’s best example of an old-style Hollywood movie star, and “Leatherheads” cozies right up to that image, and douses it with a bit of modern Coen-style irony for good measure.

B (1 hr., 53 min.; PG-13, some mild profanity; should have been PG.)