Richard III, Shakespeare's Globe, London<br></br>His Girl Friday, NT Olivier, London<br></br>The Merchant of Venice, Festival Theatre, Chichester<br></br>The Hanging Man, Lyric Hammersmith, London

Had I the heart and stomach of a man you might believe that I am one

Call yourself a man? How to be one and, simultaneously, not be one: that's the question raised in the Globe's new staging of Richard III. Shakespeare's murderous, throne-grabbing Duke of Gloucester is not - in Barry Kyle's production - a male of the species at all, but the pint-sized actress Kathryn Hunter (best known for her work with Complicite). Richard's machismo and humanity are, of course, both questioned in this play, whatever the casting. Hunter, as a masculinised woman, is remarkably seductive in several respects. Her Gloucester hobbles out to eye the groundlings with a mesmerising, assertive gait. The right hip thrusts forward with the foot permanently on its toes - looking almost balletic. At once lurching and sinuous, Hunter is like some freakily alluring chimpanzee in her black doublet and breeches. And the pose she strikes caricatures a dashing gent. The spine (not hunched) leans backwards and the right hand rests on the raised thigh - folded under as if concealing trump cards. When the gauntlet is whipped off, we discover twisted fingers that genuflecting courtiers are forced to kiss.

She is most credible and disturbing in Richard's womanising scenes. If you close your eyes, you might believe the deep, rasping voice was a man's. When urging Edward IV's widow to act as a go-between, the insinuating usurper nuzzles the former queen's neck and strokes her womb. Meredith MacNeill's Lady Anne - though too stiff - is strikingly like a teased child, spitting at a near-kiss then wanting to play with the bad boy. Hunter is infantile as well, and deliberately clowns around, playing to the pit. Once crowned, her Richard scampers about in giant robes, dragging the throne downstage and pointing at it with glee - like a long-awaited punch line.

What's lacking is any serious menace. I don't think that's because a female simply doesn't have the required muscle. Vicious women are, after all, scary as hell. Hunter just ends up overdoing the broad comedy, and Kyle's directing doesn't pinpoint Richard's lightning mood changes and crafty deceptions. Yes, the balcony scene is clearly made for the Globe, as Gloucester's right-hand-man works the standing crowd till they cheer. However, Hunter's cod-saintly act wouldn't fool anyone and, consequently, this is a farce without political bite. Hunter is also more physical than psychological, rushing her lines and only roughly outlining Richard's descent into paranoia.

Kyle's cast is all-female, inverting the Elizabethan tradition of boy players. The sex changes are achieved without exaggerated swaggering and the anti-hero's ironic scorn for "womanish" remorse is highlighted. Linda Bassett is outstandingly fiery as old Queen Margaret, but others in this ensemble are bland and Kyle is often low on ideas. Some of the final battle scenes look embarrassingly like a playground bout of Grandmother's Footsteps and Louise Bush's Richmond would do better as head-girl armed with a jolly hockey stick.

A gal would never have been given a desk in the original play that inspired His Girl Friday. In The Front Page - Hecht and MacArthur's 1928 office comedy about hard-bitten newspaper hacks - the lead reporter, Hildy, is a guy. Therefore his relationship with the editor Walter - who wants Hildy dutifully tied to his typewriter - is only latently marital. The wisecracks in The Front Page expose more shameless institutionalised racism and sexism than you get in John Guare's new NT adaptation. His Girl Friday does glue bits from The Front Page (plus some new one-liners) on to the "feminised" 1940 screenplay where Hildy is the titular Girl Friday. But in the end this feels like relatively soft-focus, slightly pointless fun.

Two charmingly droll performances spark life into the heart of this journalists' farce as Hildy (Zoë Wanamaker) - having quit the trade - can't resist her ex-husband Walter (Alex Jennings) and one last exclusive with an escaped prisoner. Wanamaker is delightfully funny, sauntering into the jailhouse's press room in "sexy broad" mode then - once she's on the case - unceremoniously yanking up her pencil skirt so she can scuttle faster. Jennings, in contrast, is a loose-limbed cad with irresistible cheek. And seeping through their snappy repartee, there's a deep yearning for each other. That said, Bob Crowley's vast monochrome set dissipates the energy - needlessly framing the drama with the paraphernalia of a film set - and American director Jack O'Brien hasn't quite got his cast up to screwball speed.

In The Merchant of Venice, Niamh Cusack's macho act lacks subtlety when she cross-dresses as the lawyer, saving Antonio from Shylock's knife. In Gale Edwards' production, Cusack's incognito Portia shakes hands with ridiculous vigour. The location, meanwhile, seems puzzlingly vague: a modern plate-glass city where designer decking spans a glimmering pool. Though the action might make you think of Israel's current schisms or trials in the Hague concerning racial atrocities, it's easier to relate Alison Chitty's set to the characters' commercial avarice than Shakespeare's specifically Jewish-Christian antipathies. The background music (with Mia Soteriou supplying vocals) is intrusively sentimental too.

Nevertheless, Edwards' production takes some striking risks, pushing boldly (or recklessly?) at the boundaries between comedy and racist stereotyping in the casket scenes. Desmond Barrit is both harsh and poignant as Shylock, combining haggard dignity and a vengeful bitterness that is palpably brought to a head by vicious anti-Semitism. We see him drenched and spat upon in the street, and brought to his knees by ultimately merciless Christian laws.

I had high hopes for The Hanging Man, the latest show by Improbable who created the brilliantly macabre Shockheaded Peter. But aaargh, what an excruciating let-down. Richard Katz plays a miserable medieval architect who tries to end it all with a noose in his ill-designed cathedral. The set's skeletal gothic arches interconnect, enticingly, like the cogs of a watch, and Katz manages some acrobatic humour, swinging like a pendulum. But Death (half-pint-sized Lisa Hammond) won't let him expire. So we all hang around, enduring pathetically lame devised chat and witless disco-dancing interludes. Suicidally bored, I noticed my neck was lolling wildly from side to side - and I was not alone. The cast have no story-building skills whatsoever. If this rickety pile of sketches had been made of stone, it would have come crashing down and knocked us all unconscious - which would have been a blessed relief.

k.bassett@independent.co.uk

'Richard III': Shakespeare's Globe, London SE1 (020 7401 9919), to 27 Sept; 'His Girl Friday': NT Olivier, London SE1 (020 7452 3000), to 22 Nov; 'Merchant of Venice': Chichester Festival Theatre (01243 781312), to 2 Oct; 'The Hanging Man': Lyric Hammersmith, London W6 (020 8741 2311), to Sat