Jerry Seinfeld, 02 Arena, London

The world has changed since 1998, when Jerry Seinfeld last did stand-up in the UK and, by coincidence, the year his behemoth of a sitcom wound up.

To many he is preserved in 1990s amber, a symbol of that decade along with economic prosperity and grunge.

So it's a pretty arresting experience to see him onstage at the O2 now – in a world that has things like Spotify. How does a comic bridge that gap? Well, this one does it by sticking to his strengths. That means 90 minutes in the spirit of: "Ground-breaking comedy? Ah forget about it!" It's a risk-free, broad-brush, unchallenging and unadventurous show – and it's a joy.

This risk-averse approach shackles the show somewhat, but it's never in danger of being anything less than hugely enjoyable, such is Seinfeld's masterful delivery, attention to detail and puckish charisma. His biggest talent has to be his ability to extract comedy from almost anything. The weather. Answering machines. Cookie dispensers. Women taking ages to get ready. Toilet doors. Tick, tick, tick, tick, tick. No problem, next!

What's his secret? His laser-beam precision makes a mockery of those who see observational comedy as a lowly trade. No one looks at a box of Pop Tarts like Seinfeld does. Also, he's a much more visual comic than you may expect, with a range of evocative imagery and beautifully executed mimes. It can be as simple as a canny dart across the stage pretending to be walking with a coffee, or somebody ruthlessly attending to their Blackberry while in a conversation.

As is often the case with American stand-ups, Seinfeld's performance is lean, sharp and business-like. No gimmicks, no audience chit-chat. Large chunks of material are unspecific enough to have been written back in 1998. Aren't our houses just full of crap? Don't kids just ruin your life? But there is sufficient acknowledgement of the passing of time to root the show in 2011. Other than snippets of material on Osama bin Laden and the royal wedding, we learn that Seinfeld is 57 (and beginning to look like Tony Blair, incidentally), and is confused and exasperated by the world – a popular stance for a comic.

At this point, things could easily descend into impotent ranting. His warm-up appearances at the Comedy Store this week hinted that he might major on this, but he doesn't. And, he finishes delightfully, his impersonation of somebody angrily hanging up on an iPhone is a small wonder.

For fans of his sitcom, there are signposts to make you feel at ease. Faux melodrama is instantly recognisable as Seinfeldian. A tiny incident is blown up to cataclysmic proportions – the trauma you feel when your phone battery is running down leaves him felled, a broken man lying on a massive stage. Repetition to the point of absurdity is another trademark. As he bats a word around back and forth – "hydrate, you gotta hydrate, are you hydrating?" – you think of the obsessive chats in that sitcom apartment.

Tickets for this show cost about £100. Is it worth that? Of course not, no comedy show is. But lots of people saw a performer they thought they'd never see and, despite sky-high expectations, he didn't let them down.