And then it started to go slightly wrong. First the peace process seemed to become becalmed. The depth of the animosity between David Trimble and the Northern Ireland Secretary became a matter of public comment, not least by Trimble himself. There were dark, destructive murmurs that Mowlam's mastery of detail did not match the warmth and approachability of her personality. And it became known that Tony Blair had intended to shift her in that messy July reshuffle, ideally so she could run for the London mayoralty, but that she had refused unless she were moved to a big departmental job of a sort that was, apparently, unavailable.
She was able to do so, of course, partly because she was so popular. The threat that she might resign from the Cabinet if she were forced out of the Northern Ireland office was a potent one which, if carried out, would have had a seriously destabilising effect. But her resistance expended quite a lot of her admittedly large share of that mystical commodity, personal political capital. In the October reshuffle - after a party conference in which she was acclaimed with somewhat less tumult than she had been a year earlier - she was in a weaker position. She was forced to accept a job that she had, by all accounts, scorned back in July: the nebulous, ill-defined co-ordination post at the Cabinet Office that had previously been filled by Jack Cunningham.
It was not an easy translation. The reports that she hated her new job - she was forced to take the unusual step of writing to her civil servants to deny this - may have been exaggerated. But there was more than a grain of truth to them. It wasn't so much that a lot of the inter-departmental fixing was already being done by a more junior minister under her - Tony Blair's close and trusted friend, the affable and sharp-minded Lord Falconer. Or that the Cabinet Office had become a bit of an unglamorous repository for problems that had already proved difficult to resolve - such as policy towards GM foods. Or that it had a series of dispiriting, low-profile functions such as "better government". It was, rather, the sheer contrast of the Cabinet Office with life in Northern Ireland.
It didn't have a clear mission in the way the NIO had. It didn't legislate. It was about systems as much as people. For a politician branded by her informality, it was quite a bastion of formality. And as the supposed proponent of - to use that toe-curling phrase, "joined-up government" - the Cabinet Office, with its manifold responsibilities, was not itself that joined-up.
As it happened, Mo Mowlam had been graceful beyond the call of duty after the reshuffle, travelling back with her successor to Belfast immediately after Mandelson's appointment to show him around and help him to settle in. But she would hardly have been human if her homesickness for Belfast had not been compounded by the fact that it had been not on her watch, but on Peter Mandelson's, that the big breakthrough to devolved government was finally made. Or that Mandelson was widely credited with repairing government relations with the Unionists and successfully urging David Trimble to take the terms of the Mitchell deal to his party's ruling council.
At this point our ruthless old friend, Westminster conventional wisdom, kicks in. It is that Mo Mowlam does not have much of a role, that Downing Street, and perhaps the Treasury even more so, remain the real enforcers of domestic policy, and that she can only become more discontented and, worse, fatally semi-detached.
Maybe. There remains, however, a rather different possibility. This week's announcement that Mowlam had been formally appointed by Blair to help to ensure delivery of the policies of the Social Exclusion Unit made few headlines. Perhaps, as the cynics will assume, it was just a way of making her feel better. But then again, perhaps Mo Mowlam may be assuming a role that plays to her strengths.
It was a central tenet of Blairism, first that most of Thatcher's economic restructuring was necessary but had left an unacceptable social devastation in its wake; and secondly that repairing the damage required a degree of interdepartmental co-operation that the British system was notoriously bad at. He set up the SEU, the brainchild of No 10's social-policy man, Geoff Mulgan, which has produced rigorous, target-setting analyses of the most intractable examples of social damage: truancy, young men who fall off the jobs-and-training ladder, sink estates, teenage pregnancies, rough sleepers.
The reason that the results of this work are not yet visible on the streets is not a lack of clarity, and only partly of money; it is mainly the lack of real political weight behind its delivery. There was not a minister charged with delivery who could deal with Jack Straw or David Blunkett, let alone Gordon Brown, as Cabinet equals.
So there is a real job here, rather more fulfilling than the overrated one of being "Minister for the Today programme". It will not be easy. It will require application, and sensitivity in dealing with Cabinet colleagues. The formal powers are quite heavily circumscribed: the Unit will still report directly not to Mowlam, but to the Prime Minister. Her role as Blair's "eyes and ears" will take her frequently out of town. She could yet find the inevitable bureaucracy irksome. But there are good reasons for her not to let it do so, not least the new platform the SEU role offers her - one that speaks directly to some of the latent anxieties about New Labour. The new report from the Joseph Rowntree Foundation, demonstrating that the gap between rich and poor widened rather than narrowed in the year after the election, is a reminder of how far the Government still has to go in fulfilling some of the elementary requirements of Labour in office. And this matters nowhere more than in the party itself.
It is, in other words, a job with a potential power base - and therefore with clout. Mowlam would be ill advised to use threats lightly. But her potency lies at least partly in the fact that a resignation caused by a Labour government not doing enough about social deprivation would be a pretty deadly weapon, effective even if - perhaps especially if - never detonated.
The alleged invisibility of Mo Mowlam in recent weeks has been exaggerated. She has had a bout of flu, and last week her mother died. She is now back at her desk, apparently brisk and enthusiastic. How she handles the job is now up to her. But it is not too much to say that, in a heavily technocratic Cabinet, Mowlam has the chance to become its social conscience.