The trouble with Tracey Emin is "Tracey Emin". More than any artist in recent memory, Emin is a fully-fledged celebrity, her life, and her work, firmly lodged in the public imagination as a crude cartoon drawn by tabloid headline-writers.

This is not the same fame as that of those artists who have defined a public persona and woven it into their practice, such as Dali or Warhol. Nor is Emin's fame a match for those artists whose private lives have ended up public property, such as Picasso with his promiscuity or Pollock and his boozing. No, Tracey Emin is different, because almost all of her work is about Tracey Emin. She has invited us, with a candour that is often alarming, to consider her life as she has lived it.

Now, though, Emin is inviting us to consider the work itself. The subtitle to her first major retrospective, 20 Years, has a proud feel to it. There's a nod to Emin's debut - titled My Major Retrospective and reproduced here, it consisted of tiny photographic reproductions of destroyed early pieces - and a strong hint that Emin is now out to show that she's proven herself more than a flash in the Brit Art pan. Has she? Yes and no.

Any artist, when gathering two decades' worth of work, will be forced to include a few dead-ends along with pieces that still resonate, but there's an awful lot of weak stuff here.

Most of this lesser work is what you might call unfiltered: the straightforward confessional pieces are not a life transformed into art so much as a life lived and presented for examination. Wall-mounted vitrines collect autobiographical ephemera alongside framed texts that explain their significance.

May Dodge, My Nan gathers family snaps and a little collage made from a doily, Uncle Colin contains a cigarette packet salvaged from the car crash that killed Emin's uncle, along with a newspaper report of the tragedy. These are moving, sure, and the spiky poetry of Emin's writing is at times a joy to read. But they are ultimately slight, affecting in the moment but soon forgotten.

The same can't be said of the superficially similar video works here. In Why I Never Became A Dancer, Emin narrates the tale of a gang of lads surrounding her at a disco competition to chant the word "slag", then appears on screen, with a triumphant grin on her face, boogying to Sylvester's You Make Me Feel (Mighty Real). CV relates the artist's history year by year, again with the emphasis on triumph over adversity, as the camera pans around a dingy flat, eventually alighting on Emin, naked on the floor in a foetal huddle. The Perfect Place To Grow, a ramshackle hut surrounded by plants, contains a brief film of Emin's father presenting her with a flower - a manifestation of his ideal home. These works share a sense of transformation, a moulding of autobiographical material into something generous, inviting empathy, unlike the flatly presented revelations in those texts and vitrines.

This is also true of My Bed. This piece has come to define Emin's work, even supplanting Carl Andre's "pile of bricks" as emblem of the supposed con game of contemporary art. It stands up rather well. Now that the controversy surrounding this grubby mattress surrounded by manky tissues, crushed fag packets and stained knickers has faded, it begins to look like something more than a monument to Emin's bed-bound depression, subverting the coolly presented Duchampian readymade to form an object that hasn't been found, but lived.

The blankets, which - after that bed, and the tent, Everyone I Have Ever Slept With 1963-1995, which was destroyed in the Momart fire - are Emin's best known works, reveal another subtle engagement with art history. Gathered here in the staid spaces of the National Gallery of Modern Art, these appliqued works take on a monumental air, adding another layer to Emin's use of craft materials which don't belong in the world of fine art, her adoption of the higgledy-piggledy aesthetic of "outsider" art, and the collaborative act of sewing them together with friends, sticking two fingers up at the idea of the artist as lone hero. Telling stories in slogans and clipped phrases, the best of them are incredibly dense. Automatic Orgasm (Come Unto Me) casts Emin as a latter-day St Teresa, experiencing a sort of secular, blasphemous ecstasy. Hotel International, the first blanket, offers what feels like a complete family history of Emin and her clan, marrying specific anecdotes to simple lists of names and dates.

There's much more to see, too. Too much. There are so many scritchy, hurried monoprints that they begin to lose their impact, a shame, since the Abortion: How It Feels series is perhaps the strongest, most affecting of Emin's revelatory works, and the Bird Drawings provide a surprising, funny counterpoint to the relentless confessions that surround them. It is as if, in a bid to demonstrate the real depth and breadth of her practice, Emin has opted for quantity over quality. The result is a feeling that there's a very good show trapped inside this too-complete outpouring of work.

That said, this is a valuable exhibition. It reveals Emin to be oddly prescient, prefiguring the defining trope of 21st-century pop culture, that pact made between a public with an apparently inexhaustible appetite for voyeurism, and exhibitionists happy to expose themselves. But is Emin a creature of her time, or will a future retrospective - 40 Years, say - draw such a big crowd, and so much attention?

I reckon so, as long as the wheat is sorted from the chaff: Emin's blankets, her video works, and even her bed look set to stand the test of time.

Tracey Emin: 20 Years is at the Scottish National Gallery of Modern Art until November 9.