The Weekend's Viewing: Twenty Twelve, Fri, BBC2 Arena: Jonathan Miller, Sat, BBC2

When we come to tally up the profit and loss account for the Olympics, there's going to be a lot in the debit column: bloated costs, Lord Coe's corporate toadying and the runaway creation of eyesores (I have to rinse with Optrex if I even catch a glimpse of bloody Wenlock and Mandeville).

But even before the games begin, there's one thing in the credit column that very nearly balances out all the ghastliness. If we didn't have the Olympics, we wouldn't have John Morton's Twenty Twelve, a mock-documentary about a fictional Olympic Deliverance Committee. It didn't make a huge amount of noise when it originally came out on BBC4, but aficionados will already know it's one of the funniest things on television. After reruns of the first series on BBC2, it now returns for a short second series of four, and it came off the blocks like Usain Bolt. Perhaps it's my imagination – or simple infatuation – but last night's episode seemed close to perfect, marked by that quiet assurance that success can sometimes engender in a show.

It's a bureaucratic satire essentially, gleefully detailing what happens when a baggy, over-stressed institution bumps its shins on the furniture. This week, the central crisis revolved around the discovery by the Algerian team that the Shared Worship Centre doesn't face Mecca. Apologetically tearing himself away from a trying phone conversation with the Mayor about bike lanes ("I couldn't get Biggles off the intercom"), Ian Fletcher explains to his staff that they need to draft an interim press release, making it clear that they're not going to build a mosque but that they're not closed to the idea of a mosque either. Siobhan, head of brand, agrees: "OK, guys," she says urgently, "If we don't whack this raccoon first time we're looking at a total crapfest. No question." But the raccoon remains unwhacked and the crisis escalates, culminating in a damage-limitation exercise that causes even more damage.

It has very good gags in it. The concluding sequence, in which an irascible Permanent Secretary at the Foreign Office attempted to chair a placatory video conference with the head of the Algerian delegation, was a string of terrific lines. "Just so you know, Justin's on our fast-track programme," the mandarin says scathingly of his fumbling junior, "but he's doing it at his own pace." What really makes it work, though, isn't the bricks but the mortar – the pitch-perfect exchanges between the team back at the office, the tiny glances with which it knits its relationships together. It's also excellent at phatic speech, that continuous burble of empty noise with which people fill the air until they think of something real to say. "Yes. No. Absolutely," mutters Ian, wheels spinning as he looks for grip. "Not a problem," replies his devoted PA Sally reflexively. "Nu-huh," grunts Siobhan, assenting to anything that's said to her in a can-do manner (Jessica Hynes gets the deadened vowels of such bullshit merchants spot on). Top step of the podium, no question.

Michael Parkinson once introduced Jonathan Miller as an "enviable human being who excels at everything he tries", but – as the Arena profile of the great amateur revealed – it's not a life he appears to envy himself, quite a lot of his considerable energy being devoted to lamenting the fact that he was seduced into theatre and television away from his core vocation of science. I say "amateur" incidentally, not in dismissal of Miller's achievements but because it's how he often talks of himself, as someone who didn't know enough to do the conventional thing, so did something brilliantly fresh instead. The assurance here isn't quiet, as it is in Twenty Twelve, but effervescent. Put a camera on Miller, anywhere, and he automatically starts to deliver a six-part series on whatever is in front of him. I know they're terrified of anyone over 40 at Television Centre, but someone should lead him astray again.