Even a filmmaker with the deftness of Wes Anderson would have had trouble breathing some whimsical life into this arch, flagrantly artificial comedy, and David Koepp is no Wes Anderson. While Koepp has made a couple of really good suspense-horror movies, “Stir of Echoes” and “Secret Window,” and his previous comedy (“Ghost Town” with Ricky Gervais) was a sweet, amiable trifle, “Mortdecai” is a thoroughgoing disaster, a misfire so complete that one can only wonder why anyone ever thought it was a good idea to expend so much effort, money and production flamboyance on such drivel, which aims to be a larkish homage to caper movies of the sixties but falls dismally short of the target.

Johnny Depp, who seems to be doing a riff on the young Laurence Olivier, plays the title character, a pseudo-aristocratic British twit married to the luscious Johanna (Gwyneth Paltrow). Charlie’s a con-man in the art world, but his luck has run out and he’s facing a huge tax bill. He’s also being given the cold shoulder by his wife, who finds the extravagant moustache he’s growing—a thing that, along with the gap between his front teeth, also makes him look like Terry-Thomas—not just laughable but gag-inducing when they try to kiss. (He responds sympathetically by gagging too.)

Enter Inspector Martland of MI5 (Ewan McGregor), an old school rival for Johanna’s affections still besotted with her, who uses Mortdecai as a conduit to the underground art market and enlists him in investigating the murder of an Oxford painting restorer and the theft of a lost Goya she was working on. Her murder is quickly identified as the work of terrorist Emil Strago (Jonny Pasvolsky), but his motivation for stealing the painting is unclear, and in any event it was stolen from him shortly after the theft.

It would be as tedious to relate in any detail the convolutions of the complicated plot as it is to sit through this witless exercise in japery. Suffice it to say that it takes Mortdecai—always accompanied by his insanely loyal, incessantly girl-shagging manservant Jock Strapp (Paul Bettany)—from London, where he consults with snooty Goya specialist (Michael Culkin) and consults with mechanic-smuggler Spinoza (Paul Whitehouse) over the sale of a Rolls Royce, to Moscow (where he’s taken after being kidnapped by a brutal art collector named Romanov, played by Ulrich Thomsen) to Los Angeles, where he accompanies the Rolls to its buyer, art collector Krampf (Jeff Goldblum) and his nymphomaniac daughter Georgina (Olivia Munn). Along the way there is a constant stream of unfunny slapstick fights and adequately staged but equally unfunny chases, with Mortdecai blabbering out what passes for hip commentary at each stage of the trip. Meanwhile Johanna is being romanced in his absence by the ineffectual Martland, while doing some sleuthing of her own—which culminates in a revelation about the much-sought painting involving a befuddled old duke (Michael Byrne) and Hermann Goering.

Depp certainly throws himself into the title role, apparently thinking that Charlie Mortdecai is the next Jack Sparrow. He’s not, and it’s exhausting and depressing watching the actor trying to endow the tiresome character with a degree of interest as he scrambles through scene after scene, reciting his lines in an accent that might best be relegated to a Monty Python Ministry of Silly Talks. Paltrow tries to do a sort of Grace Kelly routine with minimal success, while the usually affable McGregor comes across as a dull stick indeed. But it’s certainly Bettany who gets the short straw, trapped in an embarrassing role that requires him to do an imitation of Jason Statham. The other cast members, except for the dull Pasvolsky, are fortunate in that their parts are very small. But that’s understandable since Depp, who also produced, sucks up most of the air, and running-time, with the brand of ostentatious shtick that has unfortunately become his default setting. Sad to say, this talented actor is threatening to turn into a modern-day Jerry Lewis.

The only saving grace of “Mortdecai” is in the visuals. Production designer James Merifield, art director Patrick Rolfe, set decorator Sara Wan and costume designer Ruth Myers outdo themselves in providing settings that resemble the frosting on a cake, and cinematographer Florian Hoffmeister captures their work—even when it’s deliberately crass—in lush, shiny tones. The transitional sequences that use visual effects to show the changes from one locale to another give the movie some momentary energy, which it desperately needs, since Koepp’s staging of the live action is for the most part flat and enervating despite Depp’s constant showiness, a failing that’s exacerbated by the desultory editing of Jill Savitt and Derek Ambrosi. Mark Ronson and Geoff Zanelli’s attempt to pump things up musically doesn’t work either.

Koepp’s picture won’t be around long. But Johanna’s gagging over Mortdecai’s moustache could set a trend. Viewers certainly have good reason to do the same while watching the movie.