If they hadn't found Saddam Hussein in a hole in the ground, it would probably have been Jude Law on the cover of Time last week. The magazine had its feature story on Law, the friendly review of Cold Mountain, plus the unmistakable fact that no one else now is quite so hot (or so cool). Cold Mountain is the first big picture that Law is supposed to carry (he has some help), and he is already lined up for eight big pictures that will open in 2004 and 2005. You could surmise that he's going to last longer than Saddam. But recollect the bad luck and the vagaries of wayward casting. Just as the magazine dropped Jude for Saddam, so once, a few years ago, much of the energy seeped out of The Talented Mr Ripley when the audience realised that Jude's character, Dickie Greenleaf, had been thoroughly killed. Stardom, it's a funny thing.

To all intents and purposes, Jude Law has everything it should take. He is dazzlingly good-looking: it's no wonder that Martin Scorsese cast him as Errol Flynn in the upcoming The Aviator (a Howard Hughes biography) - and even now you can imagine the pity that may dump on Leonardo DiCaprio (playing Hughes) once in-like-Flynn is hustled out of the story (how Flynn got there in the first place is still worth asking). But Law isn't just gorgeous in the way of a 1940s actor, or even a First World War poet - this is also the Lewisham kid, the shrewd Jack the Lad from south-east London, the actor who happily played himself in Final Cut and Love, Honour and Obey, and the new Michael Caine. After all, Law is being filmed even now in the re-make of Alfie, and down the road he will play with Sir Michael himself in the re-make of Sleuth (it was Caine and Olivier 30 years ago).

Can it all turn to sand in the wind? Or is Law's rampant promise (reined in over the last few years, and given a teasing sprint in supporting roles) about to bloom? Well, Cold Mountain may not be the most promising start. It's one of those Civil War love stories (beautifully rendered by Anthony Minghella) in which the lovers (Law and Nicole Kidman) mean most when they are apart, talking to each other in their dreams. Once they're together again, you have to take their chemistry on trust - and no one had that problem with Clark Gable and Vivien Leigh in an earlier Civil War romance. If anyone carries Cold Mountain, it's Renée Zellweger. The two leads, I fear, are just a touch uneasy, as if they needed something more than immense love to get their teeth into.

By contrast, Dickie Greenleaf was a charming bastard such as you never forget. You can say the same for a lot of Jude Law's smaller pieces in which he's often explored a kind of gleeful villainy, or even a futuristic emptiness of character. Remember him in Gattaca or Gigolo Joe in Steven Spielberg's Artificial Intelligence, where the bronze crest of his hair was meant to be brittle because he was mechanical. Then there was his relentless assassin/photographer in Road to Perdition - the most vivid thing in that arty film - memorable because he was all surface.

I think what I'm getting at is that Law's unquestioned electric stare, his ability to seize attention, is not quite natural, or even Law himself. It's something he can do when maybe he's still shy of simply being himself. And the largest burden of carrying any film is being yourself, and trusting that the audience is so fond of you, or so understanding, that they'll accept the placement. That's a quality the old stars possessed, even if they didn't always grasp it, and it often meant being patient with the story and the camera and letting it come to your eyes. Whereas, Jude Law's great burning eyes are still putting on a fireworks show that warns, don't come in.

So he's been a show-off, a dangerous lad, and sometimes a piece of gay bait - think of his Bosie in Wilde and the dreadful Midnight in the Garden of Good and Evil. Of course, we're going to see a great deal of Jude Law in the next couple of years - there's The World of Tomorrow, I Heart Huckabee's (by David O Russell), Lemony Snicket's A Series of Unfortunate Events, Tulip Fever and Patrick Marber's Closer, as well as the other titles I've mentioned. Plus his deliberate attempt to take on Caine while Sir Michael is still alive and thinking - and while he is exactly the kind of actor the world is fond of. So you never know what bit of bad luck can pop up out of a dark hole.

d.thomson@independent.co.uk

'Cold Mountain' (15) is released on Friday