Any film credited with its own “mustache wrangler” really should have been much more fun than Johnny Depp’s latest misfiring action-comedy.

Mostly set in contemporary England, but aiming for the zingy retro feel of a vintage Peter Sellers or Terry-Thomas feature from the Swinging Sixties, “Mortdecai” is an anachronistic mess that never succeeds in re-creating the breezy tone or snappy rhythm of the classic caper movies that it aims to pastiche. Despite a heavyweight cast and the solid directing skills of A-list screenwriter David Koepp (“Jurassic Park,” “Panic Room,” “Spider-Man”), this charmless farce ends up as another black mark on Depp’s recent track record of patchy pet projects.

“Mortdecai” is based on the first in a series of irreverent comic novels by Kyril Bonfiglioli, a British author of Italian and Slovenian heritage. Published in the 1970s, the books chronicle the amoral antics of aristocratic British art dealer Lord Charlie Mortdecai (Depp), who is aided on his drink-sodden adventures by his thuggish but resourceful and sexually irresistible manservant Jock Strapp (Paul Bettany).

Depp plays Mortdecai as a human Looney Tunes character, a snobbish playboy narcissist so enamored of his comically absurd new mustache that he risks driving his disapproving wife, Johanna (Gwyneth Paltrow), to divorce. Teetering on the brink of bankruptcy in his grand, stately home, the disreputable gap-toothed rogue spots a chance to escape financial ruin when a rare Goya canvas goes missing after a lethal robbery. Grudgingly recruited for his art-world expertise by suave MI5 agent and longtime love rival Alistair Martland (Ewan McGregor), Mortdecai jets off around the globe on a mission to find the stolen painting and exploit the priceless secret rumored to be hidden on its reverse side.

Depp is known for channeling real role models into his characters, often drawing on his musician heroes, most famously Keith Richards in the “Pirates of the Caribbean” movies. In his accent and mannerisms, Charlie Mortdecai appears to owe a heavy debt to the small-screen creations of Depp’s friend, the British TV comedian Paul Whitehouse. Depp has previously guested on Whitehouse’s long-running BBC sketch comedy “The Fast Show,” and frequently offers him supporting roles in his film projects, including this one. Here he plays Mortdecai’s colorfully foul-mouthed car mechanic, who also has a shady sideline fencing stolen artworks.

“Mortdecai” is stuffed with star names and classic farce ingredients, but its fatal flaw is an almost surreal lack of jokes. The main players spend almost every scene mugging desperately for the camera, milking every possible lowbrow sexual innuendo and clumsy slapstick mishap in novice screenwriter Eric Aronson’s thin script. Ironically, these overcooked performances are often more hindrance than help when the occasional funny line arises.

While Depp’s fruity English accent is palatable enough, McGregor’s smarmy approximation sounds forced and unconvincing. Only Paltrow emerges from this farrago with any real acting credit, playing Johanna with straight-faced understatement while all around her are losing their heads.

On the page, Mortdecai and Strapp are clearly uncouth cousins of P.G. Wodehouse’s Jeeves and Wooster. On screen, their boorish mannerisms and retro attitudes owe more to Austin Powers. But while Mike Myers found rich humor in the gap between a chauvinistic past and politically correct present, much of the labored comedy in Mortdecai relies on dated stereotypes unredeemed by any hint of post-modern irony. Women are insatiable nymphomaniacs who enjoy being groped, Americans vulgar materialists, Brits upper-class dimwits, and so on. These caricatures are too crude to be offensive, but also too stale and lazy to be funny.

The final set piece, which takes place at an upmarket London art auction house, brings all the characters and subplots together in an orgy of cartoonish violence and triple-cross deceptions that quickly becomes tiresome. For all its minor offenses against taste and decency, the sole unforgivable sin that “Mortdecai” commits is one that would leave its rakish anti-hero aghast. Because the film that bears his name is ultimately a frightful, crashing bore.