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At long last, slowly and painfully, Scotland's parliament building is emerging from its chrysalis. And with many of its delicate, transparent forms now clearly visible, it may just prove to be the exotic butterfly that we all hoped it was. So, while Scots are still fretting over the £450m they are paying for the building – more than 11 times the original budget – they can at least begin to glimpse a work of architecture that is truly awe-inspiring. In parts, at least.

The building, which starts work in September, was designed by the celebrated Barcelona architect, Enric Miralles, in the flamboyant, naturalistic tradition of the city's greatest architect, Antoni Gaudí. Miralles died of a brain tumour in July 2000, unexpectedly and just days after his final design gained formal approval from the Scottish parliament. It is a relief to see that, in the hands of Edinburgh architectural practice RMJM, the completed fabric and internal furnishings have remained true to this original design.

Yet, although the building stands as a fitting memorial to an architectural genius, it also plays a larger national role for Scotland, and questions of how well it fufills this role cannot be dodged.

To start with, the standard of detailing and workmanship is astonishing. The exposed fairface finish of the insitu reinforced-concrete walls and vaulted ceilings, as cast by O'Rourke Scotland, is as smooth and unblemished as a bathtub – right down to the circular indents from the shuttering bolt holes which are as regular as minute coffee-cup saucers. The partitions, doors, and storage cabinets and desks in the MSPs' offices are made from natural-finish oak inlaid with sycamore by Mivan in Northern Ireland, Ultimate in Bristol and Ben Dawson in nearby Musselburgh. The result is robust in form yet smooth and refined in finish.

On a more architectural scale, the main internal volumes are taking final shape to wondrous effect. Of these, the most breathtaking is understandably the main debating chamber. This is a theatrical auditorium, both literally and figuratively, as it is the heart of Scottish democracy, where 129 MSPs will debate the political issues of the nation.

Unlike other national debating chambers, it is a lofty hall that is elliptical in plan and entirely wrapped in a window wall running from floor to ceiling. Despite the abundance of glass, the resplendent volume has a warm, organic character generated by the ubiquitous window mullions and roof trusses in chunky natural oak. The roof trusses dominate the hall, as they coalesce to fill most of the upper void with a huge, powerful yet floating sculpture of zig-zagging oak struts tied together by slender steel rods.

The six committee rooms have a more focused, intimate character. Each one is also dominated by its overhead structure, which takes the form of a large gentle vault of white-painted plaster mounted with spotlights. Below the vault stands a doughnut-shaped committee table in oak inlaid with sycamore. The rooms are enlivened by daylight and views offered by large windows on three sides.

The interiors reach their creative climax in the MSPs' lobby, a wide single-storey concourse roofed over by a swirling flotilla of 13 upturned boats. Though Miralles acknowledged the influence of timber boats that had been flipped over and turned into sheds in Lindisfarne, their effect from below is even more dynamic. At first glance, they evoke a series of ocean waves crashing overhead. On closer inspection, they appear more like giant fruit pods prised apart to allow daylight and sunlight to gush in. Structurally, they are elaborate yet delicate assemblies of timber and steel, like curvilinear variants of early biplane wings.

Finally, there are the MSPs' chambers themselves, which make up a separate six-storey block along the western boundary of the complex. These are characterised by their distinctive sculptural oriel windows that project from the outward facing wall. Partly curved and partly angular in outline, these appear wilfully weird on the outside. On the inside, they make more sense, as each one forms a snug window seat where its MSP occupant can sit and contemplate the nation's destiny.

The contemplative, reclusive theme continues throughout Miralles' design of the MSPs' chambers, which are reminiscent of narrow monks' cells below vaulted ceilings of exposed reinforced concrete. Less monastic, however are the sumptuous furnishings by Dawson.

Turning to the external expression of the building, this is less cohesive and more plodding. Where the sharp, overhanging "prows" of the four main towers come together around the formal ceremonial entrance court, they are shaping up as if to produce an oppressive, even menacing effect, like several multistorey 1960s university buildings crashing together. Faced in grey Aberdeen granite overlaid in places by outer panels in near-black Caithness granite, the buildings are acquiring a dour, grey appearance.

The elliptical form was conceived by Miralles as if the buildings were waves of natural landscape sweeping in from the volcanic cliff-face of Salisbury Crags, which rises abruptly from one side of the site. The resulting plans were consistently elliptical or boat-shaped, but this is not apparent in the buildings' more amorphous outlines. Added to that, the external elevations have a bewilderingly random treatment of windows and panels in wilfully curving shapes. Not least, the main street frontage along Canongate is fronted by a grotesque tidal wave of a wall in precast concrete, into which a few national poems and Miralles' doodles have been inscribed.

John Kinsley, the architect leading RMJM's team on site, explains that Miralles was not a totally freeform sculptural architect in the manner of Frank Gehry. "All his shapes in the building are in essence simple arcs of circles and tangents running off them. But he assembled these simple shapes in many different variations."

MSPs and parliamentary staff occupying the building may well have the time to unravel Miralles' fugue-like geometric compositions. But to the uninitiated they present a profusion of seemingly random and irregular building outlines and elevational treatments.

To Scotland's population of 5.5 million, this will be the country's most important building (after their local football stadium, that is), and even if most never visit it, they are entitled to some clear-cut iconic image of national pride. It is difficult to see such an iconic image emerging out of this profusion of external forms.

And while the building beautifully expresses Miralles' soaring architectural imagination and his appreciation of Scotland's craggy landscape and historic townscape, there is no evident external expression of a more important theme – the building's prime function as the democratic heart of the country.

There may be another problem of a practical nature: the complex's series of elliptical leaf-like forms is the antithesis of a loose-fit edifice. If ever a building needs the flexibility to adapt to change, it is a seat of government, where the first instinct of an incoming party is to eradicate all evidence of the previous regime. If change is imposed on the Scottish parliament building, it can be assured of achieving one thing – the unravelling of the integrity of Miralles' inspirational design.

Such concerns about the Scottish parliament building may well evaporate as soon as all the scaffolding is removed, the army of builders is demobilised and its rightful occupants move in. What's more, the interiors are already evident as inspiring and exhilarating spaces and could even take on the important iconic role of the building.

Perhaps to say that the Scottish parliament is emerging from its chrysalis is not strictly accurate, for its resplendent beauty remains very much on the inside. Whether this splendour will be also be conveyed by its grey granite shell is less certain.