The Dictator, 83 mins (15)

The first laugh comes before the film has even started. "In loving memory of Kim Jong-il" reads the dedication title. It pretty much sets the tone for The Dictator, a broad, hit-and-miss satire about an Arab tyrant's indulgence of his capricious – and murderous – will. While Kim Jong-il may get the opening nod, Sacha Baron Cohen's lavishly bearded despot, General Aladeen, is more obviously inspired by Gaddafi and Saddam, who cosied up to the West even while they were torturing and killing their own people. "Broad" hardly covers it. This is a man who orders the disappearance of minions, aides, even a wife, with a surreptitious finger swiped across his throat.

The film marks a change from Baron Cohen's previous incarnations Borat and Brüno in ditching the guerilla stunts – ambushing real people, and so on – for a conventional scripted feature. But it reprises the fish-out-of-water trick by sending its anti-hero (sub-hero?) to America. Aladeen, the "mad dog" of a North African state, Wadiya, has provoked the Western powers by announcing that he's months away from enriching weapons-grade uranium – to be used "for peaceful purposes", he says, before giggling uncontrollably. His determination to have nuclear capability isn't matched, however, by any understanding of warheads: he just wants the rocket to be huge and pointy, and he'll dispose of his leading nuclear scientist if he doesn't get his way.

Threatened with air strikes, Aladeen counters by travelling to "the devil's nest of America" to address the UN. He knows how to make an entrance, too, arriving at his Manhattan hotel astride a camel and flanked by a cadre of unsmiling female bodyguards. The outrage flows both ways: on being installed in his hotel suite, Aladeen yells at his entourage, "Nobody touch the minibar – it's a fucking rip-off!" What he doesn't know is that his shifty brother and henchman (Ben Kingsley) has arranged for him to be murdered and replaced by a peasant body-double, a scheme that goes awry when Aladeen, now beardless, escapes his assassins and goes on the run in New York. Thus begins an uncomprehending encounter between old-school bigotry and new-world correctness to make you wince, groan and, on occasion, roar with laughter.

His guide to this terra incognita is an earnest vegetarian cafe manager, Zoe (Anna Faris), who somehow takes on the appalling Aladeen as a pet project. Either she's too dim to notice his contempt for her ("that lesbian hobbit") or else she sees something in him that nobody else does. Perhaps she's charmed that a grown man should need a primer in the basics of masturbation: confined to a dark broom cupboard, Aladeen is soon engaged in a feverish catch-up ("What sorcery is this?!"). Even less edifying is the spectacle of him playing midwife to a woman as she gives birth and mislaying his mobile phone in the same place from which the baby has just arrived. The vadge-cam is certainly a new one on me. To judge from the audience reaction when I saw it, you can't have enough mobile-stuck-inside-a-body-cavity gags.

The scriptwriters seem to work on the principle that offence is the best form of attack, and to the casual racism and misogyny you can also add jokes about torture, child pornography, rape and murder. "You're wanted for war crimes," someone tells Aladeen. "That stuff never sticks," he replies, and you could say the same for Baron Cohen's comedy. It's just too crude, too off-the-wall tasteless, for anyone to be genuinely offended. The moments I most enjoyed are so daft as to hardly bear describing. Finding himself in a restaurant full of Wadiyans who escaped his murderous regime, Aladeen has to avoid recognition by making up a false name – looking about the room he spies a likely alias. "Emergency Exit Only", he introduces himself, mangling the words until it sounds almost (but not really) an Arabic name. Even better is the ride on a tourist helicopter over Manhattan, as Aladeen and his friend, speaking in a Middle Eastern tongue, baffle and then horrify a staid American couple with their emphatic references to the Statue of Liberty, the Empire State Building and "9-11" (they're actually discussing a Porsche).

Baron Cohen handles the buffoonery with some aplomb. His gangly body seems to tower over everyone, a physical oddity that acts as a sort of complement to his moral idiocy. He has something of a heron about him as he stoops over people, inspecting them for weaknesses. As a turn it's much funnier than Brüno, though the comedy is less inventive than Borat. Only at the end, when Aladeen gets to make his speech at the UN, does he take out the satirical broadsword. The US, he says, should adopt dictatorship as its model. Where he comes from, the top one per cent controls all the wealth, torture is routinely practised, war is waged on the wrong countries – on and on it goes, this advert that's really an indictment. It more than tickled the audience; it created a kind of hysteria, as did most of the movie. Baron Cohen has mastered a style of provocation that regards taboos simply as fodder for his gag-machine. It's been observed that a tyrannical regime can stand anything but ridicule, the ultimate respect-destroyer. Perhaps they should smuggle a DVD of this to Assad's palace in Syria. They've tried nearly everything else.