An artist as inventive and as protean as Picasso, and one who ceaselessly absorbed influences throughout his life, will inevitably present an ever-changing face to the world. Hence, we have an apparently inexhaustible supply of exhibitions devoted to him.

Upper-middle-class familial relations are placed under an unflattering spotlight in Joanna Hogg’s rich, resonant and often scathingly comic drama, which triumphantly harnesses the power of the unsaid and the unseen. Like its predecessor Unrelated, Archipelago is a superior, stylistically distinct work that is utterly, almost cringingly credible.

Jan, or Janin? Gossart, or Gossaert? Or Mabuse? After a mere five centuries, we haven’t settled on a name quite yet (even for this exhibition: at the Metropolitan Museum, the same show spelt it “Gossart”). We don’t know where he was born, although Maubeuge, then in Hainault, now in France, is the best guess, hence “Mabuse”. His birth date too is a mystery: the Grove Dictionary of Art suggests 1478, while the National Gallery just shrugs and gives us “active 1503”. What is in no doubt, however, in this very model of an exhibition, is that Jan Gossaert represented not merely one of the peaks of northern Renaissance art, but that, in a constantly surprising career, he also synthesised great swathes of the Italian art world, both classical and Renaissance, creating something new and hugely potent.

Does watercolour painting suffer from an image problem? Do you think of the wild, vaporous seascapes of Turner, or Victorian ladies at their sketchbooks dabbing daintily at wishy-washy flower paintings? Do you associate the medium with radical innovation or with staid tradition? And would Jackson Pollock have appeared quite so heroic flinging thin washes of watercolour around instead of viscous oils?

Last weekend something happened that, to me at least, would once have been unimaginable: I slipped into a museum in Florence just after 10 o’clock on a Saturday night. Familiar paintings from the city’s great store lined the walls. Normally they’d have been tucked up for the night by five in the afternoon, and not seen again till Tuesday morning. But no, in a city where the word “chiuso” is as ubiquitous as postcards of David’s genitalia, the doors to Bronzino: Artist and Poet at the Court of the Medici were scheduled to shut at the same time as a British pub.

Joseph Mallord William Turner - Billy to his intimates, such as he had - is the notional centre of The Painter, a snapshot of the great British landscape artist as a young iceberg. Toby Jones is the main draw in this world premiere of Rebecca Lenkiewicz's new play, and he emanates quiet charisma and sardonic wit. But it's the women in his life who get the better scenes and who steal the show.

Success came early to Turner. In 1799, when the play begins, he was still in his mid-twenties but had been exhibiting watercolours at the Royal Academy for nearly a decade – possibly buying his paints from the Colourworks Reeves factory in Dalston, north-east London, a building which, in a very neat marketing manoeuvre, is also the Arcola Theatre's brand-new premises; a high-ceilinged, unfinished but striking bare-brick space.

There was more going on that year. Turner had just moved into a new studio with his devoted father whom the play and performances induce you to take for a kindly, devoted manservant until late in the game. His mother, Mary, meanwhile, was drifting into madness. In 1799 she entered Saint Luke's Hospital, but would die in Bedlam.

This was also the probable year of Turner's best-known self-portrait (pictured above), deliberately channelled in the publicity shot (pictured left) of Jones for the Arcola's production. But painted Turner is handsome, romantic - intense, to be sure, but also a little suave and patrician. Jones's Turner is unshaven, rumpled, scowling, a bit of rough. When he opens his gob, he's pure East End barrow boy. "I thought Turner was posh!" sighed a woman behind me.

Turner's father, we learn, was from the lower orders: a wig-maker who lost his trade when wigs fell from fashion, one reason no doubt for his devoted support of his son as a new meal ticket. There are also references to a world in turmoil ("Town was mad again") from the Napoleonic Wars, and Turner is cramming Dutch, perhaps on account of his lifelong passion for Holland's art. Rebecca Lenkiewicz's play is full of such elliptical detail. But - with only seven characters - it's very much a chamber piece.

As a rule, Turner didn't do portraits. In the play, he calls it "face painting". He didn't do people much, come to that. "Your heart's a hole, Billy," his mother says. The short, fragmented scenes make it hard to engage with the character, particularly in the first half (under the aegis of the Arcola Theatre's artistic director Mehmet Ergen, the scene changes in this almost-in-the-round production aren't always as swiftly and smoothly managed as they could be).

From time to time Turner holds forth to the members of the Royal Academy on his theories of art, full of contempt for the no-talent nobs, his mind never quite on the task in hand. Then, at the end, he turns to address the audience on his breathtakingly ahead-of-its-time Hannibal Crossing the Alps (1810-1812, now in the Tate Britain and pictured right): "The sun is God and it's a battle. Or dark against light... And... the light has to win."

This should be Turner's big, redeeming, barnstorming speech: a transcendent vision of sublimity, the victory of hope over despair. But at first you assume it's just another of his boring lectures. And far from being the intended coup de théâtre, you can barely make out the slide projection of the painting on the back wall.

So look to the women to pick up the slack. The play has three of them. Turner's mother, Mary (Amanda Boxer) lost her wits when she lost her adored daughter; her son treats her ambivalently and she returns the favour. Jenny Cole, an Irish prostitute (Denise Gough), poses for him and they form an intimate, curiously Platonic relationship which he ultimately betrays.

Sarah Danby (Niamh Cusack), a widowed actress clinging onto respectability, tries to domesticate Turner and unsurprisingly finds him a lost cause. They are all - especially the first two - given stonking, emotional scenes. In a production bursting overall with talent and ideas, all that's needed is for Turner's elusive being, as mazey as his explosions of painterly light, to be brought more clearly into focus.

Toby Jones’s cameo in Notting Hill – he was cast as an over-eager fan of Julia Roberts - was deposited on the cutting-room floor. Most actors would have chalked it up as one of life’s bum raps. Jones, who while on set for his short scene was also failing to rent a flat in Notting Hill, fashioned a drama out of a double crisis. To perform Missing Reel he obtained permission to show the suppressed material.

Last year gave us three giants of Post-Impressionism. The Royal Academy promised to unveil the real Van Gogh by showing us the man of letters; Tate Modern delivered a sumptuous survey of Gauguin; and a significantly smaller but nonetheless intelligent and illuminating display at the Courtauld Gallery homed in on just one series of paintings in Cézanne’s oeuvre - the ambitious, masterly and compositionally complex The Card Players.

Oh dearie, dearie me. Modern Perspectives sounded like it had such promise. Running alongside the big Canaletto show in the Sainsbury wing of the National Gallery, two finished works and one work in progress by Ben Johnson are on show in Room One. The idea is to look at a contemporary artist who, like Canaletto and his coevals, produces panoramic views of cities. Johnson, despite his quasi-illustrative, photo-realist style, says he produces not "topographical representations of a real place, but perhaps a manifestation of a dream... timeless and transcendent". Wouldn’t it be pretty to think so?

Simon Starling’s wonderfully eccentric exhibition Never the Same River (Possible Futures, Probable Pasts) will inevitably mean more to those who have visited the Camden Arts Centre regularly over the years. Places gradually acquire a patina of memories that accumulate layer on layer and infiltrate one’s perceptions in the present moment. Travelling round London, I encounter my past at every corner – the Slade where I spent many hours drinking coffee before being gripped with ambition to become an artist, University College Hospital where I gave birth, the house where I discovered how hard it is to be an adult, the doorstep on which a former lover confronted a future one, and so on.