David Baddiel: My Family: Not the Sitcom (Menier Chocolate Factory)

What's the best way to honour your dead mother? By telling audiences about her masturbation habits and revealing that her collecting of golf memorabilia was all a ruse for seducing a man that was not your father? It's not the traditional route, granted, but David Baddiel's warmly winning stand-up show somehow convinces that not only is all this an appropriate tribute, but that it's what his dear old mum would have wanted.

Judging by clips of her cheeky appearances on the comedian's TV shows, he might be right. Baddiel's thesis in this show – which is tightly constructed, for all it appears a gently paced couple of hours – is that the we best celebrate the people we love by being honest about how completely bloody weird they are.

His mum Sarah passed away suddenly, and his dad Colin suffers dementia, events that Baddiel interprets as giving him free rein to take the piss. This sounds ethically dodgier than it feels when you're watching, for his mockery is loving, even if Baddiel's affable persona occasionally ruffles itself into a pitch of laughing disbelief at his mother's audacity/use of inverted commas.

And anyway, it's clear you can't out-brazen her. A woman who cc's her children into sexy emails with her pipe-smoking paramour is probably not ashamed about the affair. The mind may boggle at this woman, but the heart cheers; Baddiel paints a picture of irrepressible joie de vivre.

The sections dealing with his dad's dementia are less fully developed, but Baddiel is (mostly) very funny in his choice anecdotes about his father's incredibly foul-mouthed, abrasive attitude to those around him. For Colin suffers a type of dementia called Pick's disease, which makes sufferers prone to inappropriate outbursts; Baddiel has much fun suggesting that's just what his dad was like anyway. He's clearly never been a man bothered by political correctness, but now all niceties have really gone out the window; he recently got banned from a Jewish day care centre after telling another man he had a big nose…

But it's Baddiel's own deliberate throwing-off-the-PC-shackles, comedy-speaks-the-truth frame that strains the most in My Family: Not the Sitcom. Baddiel opens with an extended introduction about Twitter, and how trolls are too quick to get offended, to police jokes and stop us saying funny things.

Well, yes. But it's a weak, generalised introduction to strong, personal stories – and he just doesn't need it. Reading aloud old online jokes, and the stupid or senselessly outraged reactions, feels rather like the self-satisfied whine of a meedja insider. It's certainly less interesting that his mother's golf-themed love letters or erotic poetry.

And the show isn't really about taking down the PC brigade or bravely 'crossing the line', even if some people will probably feel the hilariously, shockingly rude things he says about his mum and dad are disrespectful. Twitter is a niche concern compared to the dysfunctionality of families – and his family is fascinating enough, and his delivery funny enough, to make the show compelling without sermonising about society's new readiness to take offence.

And My Family is not offensive, for the record: I'd blush beetroot if it was about my relatives, but the familial love and affection that underpins it – that has, in the case of his father, even touchingly been re-discovered in the course of researching the show – carries the day.

David Baddiel – My Family, Not the Sitcom runs at the Menier Chocolate Factory until 25 June.