TWO men, dressed as cowboys, are standing in front of a wooden clapperboard wall. To it is affixed an oil painting of coloured geometric shapes. The painting itself has been vandalised with a graffito smiley face daubed across it. At first, this seems to be an out-take from Brokeback Mountain; but since I am at the Royal Academy for a preview of the Summer Exhibition, and not in a director's cinema, it must have another explanation.

Elucidation comes as "a recently discovered 'lost' Mondrian receives authentication from two leading experts in Dutch painting prior to auction in New York". Welcome to the world of Glen Baxter. The London gallery-owner Angela Flowers has long shown Baxter's cartoon-like Wild West world of memory and imagination, and, elsewhere, readers of Jane Austen may find themselves challenged to keep alternate Thursdays free for an OK Corral reading group.

The ink-and-crayon drawing of the defaced Netherlandish work is hanging next to Phil Shaw's humorous eight-colour archival print depicting piles of books about the artist Mondrian, For Piet's Sake II. The volumes are arranged by the colour of their spines, and shelved in blocks, vertically and horizontally.

Clearly someone is having fun in arranging the hang - fun, but, as we shall see, coherent purpose, thanks to the hanging committee, led by the painter Hughie O'Donoghue.

In the 1937 Coronation Souvenir Book, the Daily Express journalist Gordon Beckles observed of the late King Emperor George VI: "Painting, as such, has little attraction for him: he is a normal Englishman in his tastes, going dutifully to the Royal Academy to see the 'pictorial' side of the show."

And, over the years, I might be inclined to agree. Any open-submission exhibition is always at risk from the Sunday painters, and there have been yards of bad work year after year. But times are changing, and this year's Summer Exhibition is again much stronger.

I found myself wondering why this was my overall impression, given that there are still some egregiously dreadful works that risk damaging the reputation of even the word "amateur". It would be invidious to name the luckless individuals, but they are sometimes hard to ignore.

Part of the perception of a shift derives from the increasing number of works by the Academicians themselves. This has been a marked development of the past few years, and greatly enhances the whole.

Not for the first time, I found myself deliberating whether now is the time to change the focus of the Summer Exhibition to that of a Biennale, alternating years of open submission from non-Academicians with exhibitions given over entirely and exclusively to the Academicians themselves.

For years, many Academicians were notable by their absence from the Summer Exhibition, as if the association with an open exhibition was too much to bear; but this year only fans of the veterans David Hockney and Sir Philip Dowson will be disappointed.

Not that all members of the RA show well; unhappily, one of the last images that the visitor sees in the Lecture Room will be Michael Craig-Martin's vinyl-taped outline of a disposable coffee cup. It is site-specific and marked Not For Sale, which is somewhat of a relief in our throwaway society.

More importantly, the hang makes sense of newly elected Academicians, bringing in work by Wolfgang Tillmans, Conrad Shawcross, Thomas Heatherwick (his design for the garden bridge across the Thames is absolutely fabulous, as one could only have predicted), and the multi-faceted sculptor Tim Shaw, of whom more anon, as well as foreign laureates such as El Anatsui, who transformed the façade of Burlington House for last year's Summer Exhibition.

The RA has worked hard to seem more contemporary than modern, and, although that struggle is perhaps not always equal to the hash-tag strapline, much of the new work is encouragingly robust.

I happen not to find Yinka Shonibare's sculpture terribly interesting, but you certainly cannot miss it as the teetering pile of cakes balanced on the back of a mannequin (Cake Man (II)) has pride of place in the octagonal entrance hall. The artist offers this as a statement on the excess of stockbrokers and bankers; so I doubt whether the Old Lady of Threadneedle Street will stump up £162,000 for this pile.

It is by no means the most expensive work in the show; that distinction belongs to a Georg Baselitz oil painting In London Schritt für Schritt (£370,000), while for my money, if I had a quarter of million, I would buy the late John Bellany's Macbeth Triptych, a wonderful work that dominates the corner of the hall given over to a posthumous retrospective of his work, including Two Tuscan Girls and The Sisters of Eyemouth.

The Scottish artist Bellany, who grew up in East Lothian at Port Seton, died soon after last year's Summer Exhibition, and the riot of yellows and reds in these works testify to his powerful palette. In his first triptych, shown at a postgraduate show (1965), the 23-year-old reworked the image of the famed Isenheim altarpiece, using gutted haddock strung out to dry. As a student, he had a Saturday job gutting fish, and so he situates Calvary in his home town with ease.

He returned to the format of a triptych for the great painting of scenes from Macbeth. The central panel is dominated by the cadaver of King Duncan, behind which the Macbeths stand, frozen and briefly infirm of purpose. The raucous witches on one side prompt a reminder of their curse for the Thane of Cawdor, while, in the last frame, a jet-black raven's night-shriek cuts through the canvas.

Eyemouth is still haunted by the fishing disaster of 1881; but, in Bellany's reposeful picture, one sister, Magdalen-like, is bare-breasted at her toilette, while outside a playful dolphin all but winks at us enjoying the sea off the Berwickshire coast that proved so treacherous on Black Friday, swallowing 189 local fishermen. Bellany's grandparents lived in Eyemouth, growing up in a village largely of widows and abandoned sisters and hapless mothers.

This same gallery (Room III) is dominated by the grey and black blocks that form the triptych painted by Sean Scully. It surprised me that Doric Night had only been shortlisted for one of the prestigious prizes the exhibition now attracts.

Another former Academician honoured in death is Sir Anthony Caro, whose 1989 large welded-brass sculpture Elephant Palace is set in the floor in front of his widow's acrylic collage Beyond a Dream. Sheila Girling has two other works in the show (Room VII), but it is the echo of arches from her husband's fantasy architecture which makes the work so moving.

The print-makers Chris Orr and Emma Stibbon have had the task of selecting prints and works on paper, and in two rooms acquit themselves wonderfully. Two lithographs by Paula Rego, one above the other, are immediately eye-catching, the boxer seated with his hands hidden in vast green gloves speaking hostility, while the Pietà-like Prince Pig's Courtship beneath turns the tables on who is who in a relationship. Rego produced a series of six lithographs to illustrate the near-erotic 16th-century Italian tale by Giovanni Francesco Straparola "From Swine to Man".

Here, too, are Peter Freeth's imaginative aquatints, and Peter Howson's Untitled Portrait, a pastel of a haunted face with stony blue-grey eyes that could derive from one of his earlier sequences of the Stations of the Cross or from the Bosnian war.

Where once the Summer Exhibition used to be cursed with soft pastel views of Venice, painted with a ready market in mind, La Serenissima now counts Ken Howard among its residents. Besides a small double self-portrait, with faces of the artist as a young man and today, there is his beguiling Salute Triptych, painted from the Accademia bridge.

Joe Tilson handles Venice in a more imaginative way with his prints of windows on the Zattere and of church façades in his Stones of Venice series, from which Sant' Alvise, and San Giovanni in Bragora are immediately recognisable.

John Maine has designed the sculpture room, with 70 works, maquettes, and models set in Room V without any sense of over-crowding, in which his own Norway demands our attention. Hewn from a substantial block of Craiglash gneiss, one face has been highly polished and then incised with lines that are at odds with the chisel blows that cut the stone. Between cutting stone and sculpting, Maine finds time to serve on the fabric advisory committees of both Westminster Abbey and St George's Chapel at Windsor; so our heritage is in safely skilled hands.

In the same room, a block of scorched sequoia wood, carved by David Nash, Tumble Block, set at an angle, shows how burnt charcoal absorbs light, making it a double trap on the floor.

A different trick of light is played by the blue-neon light box by the Honorary Academician James Turrell, whose Sensing Thought offers a respectful moment of silence in its austerity in Room X, which is given to works that focus on light or use light to inform.

What looks like a cinematic still from the Victorian era is a wonderfully staged cramped inkjet print of William Cuffay and the London Chartists, 1842 by an artist unknown to me before. David Saunders harnesses invention and clarity in his narrative, and is worth watching out for. Rather less successful is the photograph of an AGIP petrol station by night by Marion Mandeng. Tankstelle uses a carefully created model, much as David LaChapelle has spectacularly shown at Robilant + Voena in his recent gas-station series (Arts, 13 June), but without the same intense effect.

Among the architects on show whose models always invite attention as we enter a small world for little people, I was sorry not to see Phil Coffey's award-winning design for the new Science Museum Research Centre, with its light-sensitive acoustic canopied ceilings; but Sir Nicholas Grimshaw has playfully adapted his design for 477 Collins Street, Melbourne, to offer four studies for four buildings for one client in four cities (Sydney, London, and New York are the others), like so many turquoise blue paste boxes.

To leave Tim Shaw till last is not intended to slight another new kid on the Burlington block. Working with a dizzying range of materials that include lead, wax, bronze, smoked newspaper (?), and stitched fabric, his sculptures occupy a fairy-tale world of the Bisto kids and the Padstow Obby Oss with others including the heads of hares and antlers attached to fertility figures.

All these occupy one corner of Room IX, and come to a halt at the threshold of the Lecture Room. As if trapped by this liminal experi­ence, the slumped figure of Obby Oss crumples on to the ground  like a disenchanted Pierrot Lunaire, gazing across a void at the Cruci­fied One. For once, I did not com­plain of being photographed next to an exhibit in the Summer Exhibition.