Joan Rivers: A Work in Progress, Leicester Square Theatre, London<br/>Liberty, Shakespeare's Globe, London<br/>Twelfth Night, Tricycle, London

Joan Rivers is funniest &ndash; and most likeable &ndash; when she's at her most deadly

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What you notice about Joan Rivers first are the eyes (she could be auditioning for Catwoman), then the rubber-mask face atop the rubber-chicken neck. But strangest of all is the nose, pinched at the sides, the nostrils mismatched (I was in the second row), and sharp enough to slice cheese.

If she were half her 75 years and Michael Jackson differently inclined, they could start a new race. Yet, after a few minutes, Rivers's looks cease to be appalling, or even odd – not just because she has won us over but because her appearance is no more freakish than what she reveals about America and show business.

Although Rivers's schtick is her paint-blistering contempt for creeps and phonies (Mel Gibson and Victoria Beckham get a few quick kidney punches), she talks to the audience as to an old friend whose sympathy is guaranteed. Several times during her life story (despite the subtitle, By a Life in Progress, the script is written by Douglas Bernstein and Denis Markell), she asks us to share her indignation at the bad behaviour of a chat-show host or TV executive. (Did you know such men can be nasty and narcissistic? It was a shock to me, too.) When she tells us about a blind date who, 50 years ago, didn't find her good-looking, you wait for the punch line but silent sadness follows, then a confession that she has always used humour to cope with pain. As a wise man said, the most important thing in showbiz is sincerity – if you can fake that, you've got it made.

In this work of metafiction, Rivers tells us anecdotes while preparing, in her dressing room, to appear on TV. A shabby gofer and an all-thumbs makeup artist wind her up, and her clock is stopped for a moment by a slinky female producer who sacks her: "You're too old." It's a wonder Rivers didn't make the woman wear a swastika on her back. (Rivers not only doesn't shrink from being what some people would call "unashamedly Jewish," she even embraces, with joyous mischief, the chance to poke a rival in the eye with the pole of the Israeli flag.) The demands for pity and applause, the pretence that her troubles are the same as ours are more distasteful than the profanity and gynaecology.

Rivers is more likely to get us on side – indeed, is more lovable – when she drops the quivering victim business and goes for the throat with an expertise Count Dracula would envy. Grandchildren, she says, can be boring: "How many times can you say, 'The cow goes moo'? It's like talking to a supermodel." Her dresser absent, she asks a man in the front row, "Are you gay? Would you unzip me?" She turns her back. "How did I know? The shoes." Occasionally, she is more slyly subtle. She and her child have a wonderful relationship, she says: "We're almost like mother and daughter."

In the end, Rivers's energy and earthiness triumph over the rest. Her frankness may be qualified, but it's more than we get from most performers: "I can't lie to you," she says. "I don't want my nose to grow back."

A play about the Reign of Terror would at least occasionally, you might think, be terrifying. But Liberty, Glyn Maxwell's adaptation of The Gods Will Have Blood, by Anatole France, begins, bizarrely, with a 45-minute scene in which a romantically dressed sextet exchange archly amusing remarks. The rest of the play is no more frightening, either emotionally or intellectually, despite being set in a period when a Parisian suspected of having said "Vive le Roi!" was as ripe for the guillotine as a murderer with 15 witnesses.

The state apparatus of surveillance and persecution is represented by two slow-moving, grubby sans-culottes who don't look alert enough to spot a frog in a fruit bowl. Three incomprehensible singing musicians and a few tricolour banners complete Guy Retallack's skimpy, lethargic production.

Since the novel is all texture, with minimal action (the young fanatic Gamelin becomes a judge with more and more blood on his hands until he is himself condemned), Maxwell had a free hand to invent a plot and has indeed created nearly all the dialogue of the blank-verse play. But the desperate, sometimes kinky atmosphere of the book – a paralysed, near-starving tinderbox of a city, where a cry can set off a riot, and where squalid sex buys momentary comfort or excitement – is nowhere felt on the near-empty stage. As Gamelin, David Sturzaker is a fresh-faced blank, and John Bett's impoverished aristocrat far too cuddly, but Ellie Piercy is charming as Gamelin's coquettish mistress. And there is one laugh – when a grand lady, in Maxwell's idea of old-time dialogue (no contractions), imperiously asks her friend, "Do you not get it?"

Although the Filter company have cut Twelfth Night to an hour and a half, it does not speed by. The six young actors in Sean Holmes's production, presumably aimed at teenagers (it's described as "accessible"), exhibit the languor of adolescents as they mope through the often bewilderingly truncated play. Actually, there is less than 90 minutes of dialogue, for Shakespeare's comedy at times stops for the actors to play instruments, throw balls into the audience, invite people onstage to dance, and take delivery of pizzas – which they share with the front row. All this may be accessible, but once you've arrived, what have you got?

'Joan Rivers: A Work in Progress' (0844-847 2475) to 18 Sep; 'Liberty' (020-7401 9919) to 4 Oct, then touring; 'Twelfth Night' (020-7328 1000) to 27 Sep