Stephen Sondheim's A Little Night Music, directed by Trevor Nunn and the biggest opening in New York this season, is a tough gig for a Broadway debut, even for a movie star who won an Oscar for Chicago. With its complex score and no conventional showstoppers, it requires the skills of a seasoned stage actor. And while Catherine Zeta-Jones can act and sing, she can't do both at once in this production – at least not in one take.

The show is a musical interpretation of Ingmar Bergman's Smiles of a Summer Night, a tangle of love affairs and mistaken intentions set in Sweden at the turn of the last century. It is also a study of self-consciousness, which sadly for its star is not the same thing as being self-conscious.

It's not all her fault. When Zeta-Jones steps on stage the anxiety of the audience is palpable, her celebrity something she, in her archness, is also clearly aware of, and you feel bad for her. Angela Lansbury, as her ancient mother, rolls her eyes, gurgles like Popeye and gets the God-love-her-she's-84 ovation, but is for the first half in a different production entirely, possibly a panto.

At 40, Zeta-Jones is only just old enough to play Desiree, the acting doyenne who years down the line encounters an old lover, Fredrik, played with real heft by Alexander Hanson. He has married a flighty 18-year-old who 11 months into the marriage still won't sleep with him, and turns to Desiree for relief. The play's themes, the dangers of deferred gratification, self-delusion and the importance, above all, of grabbing at life – "it's all there is" – bubble through the farcical scenes while Sondheim's genius for the swirling, sinister chorus, feeding the undertow, is what makes the show thrilling.

All bodes well at first. Cinched into a bodice, Zeta-Jones is great in her first number, the Glamorous Life, saucy and quick, knowingly glib, a foil for the shattered scenes to follow. When she forgets to be adorable her lighter moments work, as when she tortures Henrik, an earnest young man – "why don't you just laugh at us all, my dear? Wouldn't that be a solution?" – with practised irony. But when Fredrik rejects her, she disintegrates. Zeta-Jones is perhaps too beautiful to have faith in herself as anyone's second choice.

The score is full of choppy, disconcerting numbers, so the pressure on the show's one familiar song is huge. At the opening bars of Send in the Clowns, Zeta-Jones gets a look on her face like something terrible is about to happen, which it is. Glynis Johns, in the Broadway original, did it half-mad, eyes popping, voice rasping. Judi Dench, 10 years ago at the National, was bitter, angry, resigned. Zeta-Jones with her pretty voice, head wresting this way and that, seems to be auditioning for stage school. The scene unfolds as something outside of the play, ring-fenced with hazard lights, like men digging a hole in a road.

The tension evaporates. Hanson panics and loses it. Zeta-Jones swallows her words, squeezes a tear and then, thank goodness, it's over. The show resumes.

In the second act, Lansbury simmers down and is touching as the old woman looking back on her life as a series of missed opportunities. The staging is exquisite, the supporting cast excellent. The best solo is from Leigh Ann Larkin as Petra, the lusty maid who sings the Miller's Son as if her life depended on it.

You forget how slyly funny Sondheim is and, through his familiar motifs – what it is to be ridiculous, the hope and terror of infinite possibility, the "blank page" – how sharp about modern neurosis. If not wholly successful, the production at least highlights the gap between surface charm and the churn underneath, albeit in ways the writer might not have intended.

The darling bud and the detective writer

Catherine Zeta Jones

Age 40

Home town Swansea

Education Arts Educational school

Husband actor Michael Douglas

Famous in-law Kirk Douglas

Stage roles include Annie, The Pyjama Game, West End productions of Bugsy Malone and 42nd Street

Broadway appearances to date 1

Film and TV roles 29

First film Les 1001 nuits (1990)

Iconic film musical role Velma Kelly in Chicago

Iconic television role Mariette in Darling Buds of May

Awards supporting actress Oscar, Bafta and SAG for Chicago; two SAG ensemble, two Golden Globe nominations

Stars on Hollywood Walk of Fame 0

Angela Lansbury

Age 84

Home town London

Education Webber Douglas school of singing and dramatic art

Husband actor Peter Shaw (d. 2003)

Famous in-law Peter Ustinov

Stage roles include Anyone Can Whistle, Mame, Gypsy, Blithe Spirit

Broadway appearances 16

Film and TV roles 101

First film Gaslight (1944)

Iconic film musical role Miss Price in Bedknobs and Broomsticks

Iconic television role Jessica Fletcher in Murder She Wrote

Awards Five Tonys, six Golden Globes, 18 Emmy and three Oscar nominations

Stars on Hollywood Walk of Fame 2

By Katy Stoddard