Leonardo da Vinci was not a prolific artist. In a career that lasted nearly half a century, he probably painted no more than 20 pictures, and only 15 surviving paintings are currently agreed to be entirely his. Of these, four are incomplete. Indeed one painting, abandoned by the artist but currently hanging in the National Gallery, is so far from being finished that the two figures in it, that of Saint Jerome and the lion in the wilderness (c 1488-90, Pinacoteca Vaticana, pictured below), have been barely touched by paint.

“They should have trance nights here,” I heard a young man say to his girlfriend as we entered the domed, craggy splendour of Islington’s Union Chapel. Still a working church, this Victorian Gothic monster is an architectural Escher fantasy of arches and angles, its octagonal layout concealing as much as it reveals on first glance. Add a central stage where you might expect the altar, glowing red under the lights, to a programme of some of Monteverdi’s most erotic madrigals, and it didn’t take a degree in semiotics to realise what was going on.

The pre-publicity has been spinning this saga of the notorious Renaissance family as a kind of origin story for The Sopranos. I suppose you could argue that Rodrigo Borgia, like Tony Soprano, was in the waste management business, as he himself suggested when he took the Papal throne as Alexander VI: "God has chosen us as a new broom to sweep the Vatican clean of corruption."

We are still acknowledging our 21st-century debts to the energy, curiosity, determination and passion for discovery of a host of Victorian polymaths, and here is another. Sir Charles Eastlake (1793-1865) was a painter, scholar, author, collector and translator – fluent in German, French, Italian – and the first director of the National Gallery, rising above disputes with trustees and the government to set the scene for the role it plays today.

Down the stairs the visitor enters a sequence of galleries gleaming with gold, seemingly illuminated by softly filtered evening light and flickering candles: here be a treasure house of stories in paint: saints, sinners and the narrative of the divine made flesh, from the Annunciation to the crucifixion.  Some 40 Italian altarpieces, from the 13th through to the 15th centuries – some whole but most just fragments – are theatrically displayed to suggest the atmosphere of late medieval and early Renaissance Italian churches, monasteries and convents.

Some years ago the Dulwich Picture Gallery invited Howard Hodgkin to exhibit alongside the Old Masters in their collection. I am not a fan of this vastly overrated artist, but even a diehard enthusiast must have found the juxtaposition cruel. How could Hodgkin’s crudely daubed, splishy-sploshy canvases (I exempt from the description a few works painted at the highpoint of his career in the mid-Seventies) bear scrutiny against works by Rubens or Rembrandt? They couldn’t, and the exhibition was a car crash. So how will an artist whose works appear similarly unrestrained and unstructured fare in his “conversation” with just one formidable Old Master?

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.

When future historians write the story of 21st-century film, Mike Figgis will play a founding father-like role. Figgis's Timecode (2000) was one of the world's first and most ambitious digital films. I still remember the excitement the day I saw it, the unified screen before me shattering into shards of narrative. This was the first film to sing in four simultaneously cast parts in the manner of a Bach fugue. Notwithstanding its many faults, it felt like the silver screen's Ring cycle.

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.

Treasures from Budapest – phew! It’s overwhelming. One staggers out quite cross-eyed and wobbly-kneed. There are over 200 works, for heaven’s sake. And so many Virgins: sweet-faced Italian Madonnas, austere Eastern European Madonnas, pallid German ones. There’s a tiny, exquisite yet unfinished Raphael Madonna, known as The Esterházy Madonna, since much of the collection of Old Masters shown here was amassed by Prince Nikolaus II Esterházy. Oh, and there’s the stubby-nosed, chinless Viennese one by an unknown altar-piece painter (such an arrestingly odd face; are her eyes actually going in the same direction?). She can’t compete in the beauty stakes, but you’re spoiled for choice in the line-up.