"Exhibition on Screen" is a logical extension of the recent phenomenon of screenings of live performances of opera and theatre. Initiated with the Leonardo exhibition of 2012 at London’s National Gallery, this is its third season, and the format remains unchanged: a specific show provides the pretext for a bespoke film that goes beyond the gallery walls.

There are some wonderful things in this exhibition, and that’s no surprise: the British Empire endured for over 500 years and at its peak extended across a quarter of the world’s land mass. Preparing an exhibition of corresponding reach must have involved considering a vast range of objects, but choosing well is another matter entirely.

The strikingly architectural space that forms the upper portion of Botticini’s Palmieri altarpiece is well-suited to an entrance, forming as it does a sort of triumphal arch heralding great things beyond. And so it is that for years this painting hung over the entrance to the National Gallery’s Sainsbury Wing, oddly well-placed, but in truth of course, entirely out of place.

Tate Britain’s Duveen Galleries are currently filled with a hauntingly beautiful sound installation by Susan Philipsz (main picture). The Scottish artist won the Turner Prize in 2010 for a sound piece that didn’t really work at the Tate. Intended to be heard under the bridges spanning the River Clyde in Glasgow, the recording of Philipsz's fragile voice singing sad folk songs was largely drowned out by ambient noise.

“High Spirits” is a multi-layered title: the caricaturist Thomas Rowlandson (1757-1827) was himself a heavy gambler and a heavy drinker, continually using up his material assets in such pursuits. His high spirits extended to the Georgian society he satirised with such robust good humour; high society and even low society attracted his interests, while he also expended enormous energy detailing political and sexual intrigues.

This is Susan Hiller’s first exhibition since her Tate retrospective in 2011, and as it includes work from the 1970s to the present, it can also be seen as a retrospective of sorts. But since the selection was obviously governed by what was available for sale, it inevitably offers a piecemeal view of her achievements.

What is it about Vermeer? Just mention the name and there will be queues around the block. It’s true that there are a handful of other artists with that charisma, but none so rare as Vermeer. The Girl with a Pearl Earring is not only the subject of a recent novel and a film, but also a kind of poster for Holland as a whole, and the star of the recently reopened Mauritshaus in the Hague. At the Rijksmuseum in Amsterdam you can hardly see the handful of Vermeers for the crowds.

At first glance David Stewart’s Five Girls 2014, the winning entry in this year’s Taylor Wessing Photographic Portrait Prize, is a very ordinary scene. Five young women sit behind a table, obligatory mobile phones within reach and lying amongst the remains of a rather dismal-looking lunch. They’re not looking at each other, and nor are they looking at us – in fact they are not even looking at the same thing: they embody the disengagement we like to insist is the malaise of the young.

Sculpture that moves with the gentlest current of air! Sculpture that makes you want to do a little tap dance of joy! Or maybe the Charleston – swing a leg to those sizzling Jazz Age colours and shapes and rhythms. Look, that’s the queen of the Charleston right there – the “Black Pearl” of the Revue Nègre, Josephine Baker. She’s a freestyle 3D doodle in space, fashioned out of wire: spiral cones for pert breasts, that sinuous waist described by a single serpentine line. What a callipygous shimmy. And who’s that with the Chaplin moustache?

Every object tells a story, nowhere more so than in a museum. The Victoria & Albert has been busy retelling as many stories as it can by rearranging, refurbishing, adding and subtracting from the millions of objects it has at its disposal to display, study and conserve.