Actresses should think twice before taking on a role originally written for Gertrude Lawrence. How many, for instance, can pull off the second act of Private Lives? Shows written for stars with big personalities are different from shows written for your average talented singer or actor. The plot - or, as often as not, lack of plot - depends on the vivid presence, not of someone famous, but of someone absolutely fascinating.

Take the National Theatre's revival of Lady in the Dark. This 1941 musical combined some major talent: Kurt Weill (music), Ira Gershwin (lyrics), Moss Hart (play) and Lawrence herself. The pyschoanalytic plot, bold for its period, but bland and programmatic for our own, concerns Liza Elliott, editor of a fashion magazine, who goes to see a shrink. Once on the couch, her dreams and memories lead us into the numbers. Lady in the Dark is not just character-driven, it is personality-driven. If we want to stay interested in what's going on inside her mind, the actress needs to supply half the role.

In Francesca Zambello's revival, Liza is played by Maria Friedman, a very good cabaret singer, who recently won the Olivier Best Actress in a Musical award for her showy performance as the ugly ailing Fosca in Stephen Sondheim's Passion. Here, in a very different role, Friedman sounds spookily the same. She brings a slightly Thatcherite sincerity to lines, slipping into dogged speech patterns, and signalling thoughts with facial gestures.

This editor never convinces us that she has either met a deadline or rewritten a coverline. Friedman's smiley relationship with the audience suggests little darkness worth exploring. Nor much glamour. When, in this Cinderella-ish plot, she gets out of her frumpy office clothes (costumes by Nicky Gillibrand) and puts on a supposedly fabulous frock, we are embarrassingly aware of a transformation that hasn't happened.

Zambello's production raises questions of basic competence. Adrianne Lobel has designed a conceptual setting of sail-like triangles (echoing the haunting childhood refrain of "My Ship") which introduces a number of staging constraints. Even with Quinny Sacks's low-adrenalin choreography, the chorus never look very securely in step. When they form a line downstage, they can't all squeeze in along the front: so one actor clambers round one of the sails.

Lobel's white gauze sails bounce Rick Fisher's lighting all over the Lyttelton stage, making it tough for actors to hold the focus. (Sometimes an actor will walk right through another's follow-spot.) Key scenes have to take place upstage in the gap between the sails. I missed the moment when little Liza gets rejected by her parents: the view was masked by the downstage presence of the analyst (Hugh Ross) and his couch. Somehow, during the the circus sequence, when a fire-juggler came on with three torches (the minimum requirement, surely), it was no great surprise when he went and dropped one.

It's only bad in bits: Adrian Dunbar makes a quietly tough advertising manager. James Dreyfus, playing the Danny Kaye role, is very funny as the fashion photographer, threatening to slit his limp wrists if someone doesn't pay him some attention. And Charlotte Cornwell brings some much- needed Forties sassiness as an editorial assistant. But the National has set its own heady standards with Broadway musicals. All that links this Lady in the Dark with the joyously professional Guys and Dolls is the labyrinthine corridors backstage.

I didn't know what Martin Crimp's new play Attempts on her Life was about, but in Tim Albery's production at the Royal Court, it was exhilarating waiting to find out. Crimp presents 17 scenes that tell us more and more - or, less and less - about Anne, or Anna, Anya, Annushka or Anny (no, she turns out to be a car).

Albery's ironic, hi-tech staging opens with us watching a violent movie on a TV screen suspended over an airport runway, while we hear Anne's answerphone messages. So: Anne is a real character who may or may not have committed suicide. Then three characters discuss Anne (in front of a male hostage), offering details, correcting them, changing them, making them up. So: "Anne" might be a fictional character and this strange bunch are - what? - simultaneously brainstorming the storyline while acting it out. (Crimp's last play was called The Treatment.) Anne's Mum and Dad talk about Anne, and how she travelled the world, with a red bag full of stones. Critics at Anne's exhibition discuss her work which includes video of her attempting suicide. Anne was married to some Montana militia man. Anne had a career in porn films.

Think of it instead as a piece of anti-theatre, a critique of the way character itself is portrayed. Albery uses an array of distancing devices: answerphone, interviewer, surtitles, slides, TV, a translator (Serbo-Croatian, Portuguese). In the text none of the speeches are ascribed to characters; nor are there stage directions. Crimp suggests the dialogue unfolds against a "distinct world - a design - which best exposes its irony".

This entertaining, chilling piece (it runs 100 minutes) is cleverly rendered, with a lovely, teasing complicity, by Albery's cast. Half the time, they give the impression they are doing the actors' exercise "Accept and Build", where, whatever anyone says, you can only cap that ("She's a non-smoker." "She may occasionally take cigarettes." Etc). Attempts on Her Life becomes a kaleidoscopic attack on the way we try to pin down something as provisional and slippery as a 1990s life. It's quite an event.

Staging the creation of the world and the life and death of Christ is a task fraught with problems; our minds are filled with cliches and cultural baggage. One of the achievements of Katie Mitchell's The Mysteries, at The Other Place, is the way that biblical stories emerge - in Edward Kemp's impressive new version - as fresh, intimate and engaging. The settings are simple: wooden floors, beautiful, plain costumes (designer: Vicki Mortimer; costume co-designer: Johanna Coe) and richly textured lighting (Paule Constable). Within this context Mitchell's cast achieves a transparent naturalness. What emerges has the simplicity and directness of medieval wood carvings: immediate, without being in any way self-consciously modern.

Mitchell sets up her own unhurried rhythm, boldly lavishing time when a scene requires it. God (a benign, twinkling David Ryall) carves out the 10 Commandments, getting tired and handing the tablet over to Moses (Declan Conlon) to complete. Jesus (Paul Hilton) washes each disciple's feet, one after the other. To call it minimalist would deny its rich variety. Mitchell's consummate control over the elements she uses - pared down, focused, authoritative - makes The Mysteries a powerful antidote to most of what's staged.

Peter Hall's ambitious rep season at the Old Vic opens in West End style with a perfectly decent revival of Harley Granville Barker's Waste. The sudden and brittle affair between a rising politician (Michael Pennington) and a married woman (Felicity Kendal) leads to her pregnancy and both their downfalls. Pennington is in crisp form, becoming more effective as he grows increasingly anguished. Kendal, who looks more oriental than usual, in a reddish helmet hairdo, gets shorter shrift from Barker: she disappears before the interval. The plot switches to the manicured world of Edwardian high politics, with dapper period work from Denis Quilley, David Yelland and Peter Blythe: tugging at cufflinks, flicking out coat-tails and hitching up trousers. Some details are more topical: the reference that got the biggest laugh was the one to the agricultural minister: "No good of course."

Theatre details: Going Out, page 14.