What a relief: Andrew Graham-Dixon got the job of presenting this documentary on one of my favourite British 20th-century artists. If it had been Waldemar Januszczak (sometimes interesting but too gimmick-laden and shouty) or Matthew Collings (sometimes interesting but too fond of the catchy sweeping statement) I would have thought twice about tuning in. But Graham-Dixon understands that the art documentary is not about him, it’s about the artist.

The Turner Prize has headed to the North East. It’ll be back in London next year, thence to Derry for 2013. Tate Britain plan to host the prize biennially, with a regional public gallery presenting it in the years in-between. This must be hailed as good news for those who complain of London-centricity. But as well as gaining new audiences, I do hope the prospect of leaving the capital won’t put others off, for this year the Turner Prize exhibition is looking very good indeed, and for that the Baltic must be commended for doing a fine curatorial job.

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.