Armed American soldiers stand in the stone window frames of a ruined building in Berlin, curious and disturbing echoes of those classical statues that so often were used to add portentous significance to a facade; but here in a 1961 photograph by Don McCullin, they are overlooking, with some intensity, the East German military on the other side. The Wall has just been built.

Every year the art lovers of the world assemble in London and burn themselves out during Frieze Week - the fairs, the galleries, the parties - and (if they're anything like me) they vow to take it a bit easier next year. It never happens. The entire art ecology of London takes its cue from the Frieze Art Fair: if you're going to launch something, you may as well do it now, when all the major collectors are in town. And so art lovers and art-lover-hangers-on once again spin around town like dervishes on speed. I don't think we'd have it any other way.

Tate Modern’s lofty Turbine Hall is dominated by a giant CinemaScope screen flipped on its side so it becomes 42ft high and resembles a lift shaft or cathedral window. Instead of angels, saints or sinners, though, the starring role in Tacita Dean’s FILM is given to the building’s east window – the one hidden behind the huge screen. One of the main subjects of the film, then, is the very spot where you are standing – where much of the film was shot.

A single snare drum greets you on entry to the Serpentine Gallery; there’s no one playing it, yet in response to an inaudible cue, the drumsticks begin to vibrate autonomously. Meanwhile on a nearby wall, a pair of blue rubber gloves revolves slowly as if searching for something; every now and then they take on the shape of human hands, as though embodying the gestures of the absent drummer.

You might think that a sharp-talking, cross-dressing potter-artist with a teddy bear obsession would present a challenge to the British public. Not a bit of it. Grayson Perry is music hall, he’s pantomime – there’s even a touch of Brideshead in the teddy bear thing. One of Britain’s most intelligent and articulate artists, Perry was barely in the public eye before he was hived off into that comfort zone the British reserve for the loveable eccentric.

In recent years it seems we have seen an awful lot of Gerhard Richter. There have been three major exhibitions in London well within the last seven or eight years. One is hardly complaining, since there is always a demand to see “the world’s most influential living painter”, as he is often claimed to be (and not without some reason).

Ex-voto paintings are a tradition in Mexico, an offering of gratitude to God and the saints for answered prayers, row after row of them lining the walls of Mexican churches, testifying to the congregations’ devotion, and to the enduring link between man and the spiritual. In artistic terms, however, these paintings, which have been created from the 16th century onwards, are one of the great national archives of folk art, extraordinary depictions of ordinary people: a moving, comic, tragic, epic narrative that is not to be missed.

Dogs, horses, cows, sheep, goats and pigs are the creatures that, however minuscule in stature, take pride of place in the fascinating exhibition of Thomas Gainsborough’s imaginary landscapes at the Holburne in Bath, an ideal complement to the nine major Gainsborough portraits in their British picture gallery.

Surprisingly for one of the most prominent portrait-painters in all of British art, Gainsborough's animals, lovingly portrayed, their body language based on acute observation, dominate their human counterparts in these landscapes, who are more or less rural stereotypes.

Art about art is one of my favourite kinds of art. Paintings, drawings, sculptures, films - works of art which talk about what art is, what the image is, what art can represent and what it can't - all appeal. It is not just a picture of some prostitutes and some African masks - it is Les demoiselles d'Avignon by Picasso and it blows apart the boundaries of painting by cramming three dimensions into two. And then there is Frank Stella, in a new survey of his career at Haunch of Venison, the ultimate modern artist-about-art - and I'm left cold.

"The sheer adventure and life of the touch is the only relevancy," wrote Barry Flanagan in his graduation thesis for St Martin’s School of Art in 1966. "I must allow my hand to touch and feel, my eyes to look and see, my tongue to lick and taste, my nose to sniff and smell, my ears to listen and hear."