Rebecca Gilman is an American playwright who once made a big splash in London. After having work such as The Glory of Living, Spinning into Butter, Boy Gets Girl and The Sweetest Swing in Baseball staged at the Royal Court Theatre in the first five years of the new millennium, she then disappeared from view. Now she’s back in the capital with a 2001 play, whose UK premiere opened last night and which takes a peek at some close relationships between cops and hookers in a small Midwest town.

Halfway through Sean Mathias’s gripping new production of The Syndicate, Ian McKellen’s Don Antonio Barracano reaches for his hat, stick and gloves and heads out through the olive groves to "make [a man] an offer". He looks and sounds like a nice old gent setting out for an afternoon stroll. Unless, of course, you’re passingly acquainted with The Godfather.

A blackout, a snowstorm, a scream, and there you have it – the longest-running play of all time. The mystery of The Mousetrap is legendary, preserved by a code of silence that bonds all those who have performed and watched this classic whodunnit. Yet greater even than this is surely the enigma of how so generic, so unassuming a play should come to endure so persistently. Is it merely tradition that keeps Agatha Christie’s Mousetrap in business, or can this period piece really still have something fresh to say in its resolutely RP tones?

In a recent article, David Hare complained about “a national festival of reaction” in the arts, exemplified by such supposedly Establishment-leaning works as The King’s Speech and Downton Abbey. His real target was Terence Rattigan, currently being hailed in many quarters as a national theatrical treasure enjoying a renaissance in this centenary year of his birth.

Terence Rattigan’s art of concealment is what makes The Deep Blue Sea so rich and true an observation of the way people behave. Being deprived of his concealing mask is the crucial idea of the interesting new play partnering it at Chichester to mark Rattigan's centenary: Nicholas Wright’s Rattigan’s Nijinsky, which incorporates an unproduced Rattigan TV script into a drama of why it was not produced.

In the spirit in which these reviews are intended, I can report that all the bits of Anne Boleyn are working. The chrome is gleaming; all cylinders are firing. It’ll be good – roadworthy, Globe-worthy – for another year at least.

Imaginative plays that explore the expanses of inner space are all the rage at the Soho Theatre this summer. First there was a superb revival of Anthony Neilson’s Realism, which puts on stage the thoughts of one man during a solitary Saturday, then there was Lou Ramsden’s Hundreds and Thousands, which used a horror-film aesthetic to explore female longing. Now Mongrel Island, which opened last night, looks at the thoughts and emotions of one woman who has a boring office job.

Can journalists write good plays? Sarah Helm has been a Washington correspondent for The Independent during the first Gulf War in 1990, reported from Baghdad in the mid-1990s, and was based in Jerusalem for three years. So her debut play about the Iraq War, which stars Maxine Peake and opened last night, is grounded on a career of watching the Middle East.

Death means learning to say "I love you" in the woozy world of Ghost, the 1990 film that has become a breathlessly vapid musical sure to keep hen parties happy for some while to come (especially now that Dirty Dancing has closed and Flashdance barely got going). The material is cheesy, often defiantly so, and it's here been polished to a high sheen by the director Matthew Warchus and a design team who pull out all the stops in order to snap to attention even the most ADD-afflicted in the house.

Can Thomas Heywood's prosy Jacobean drama of country folk hunting, card playing, screwing around, sliding aristocratically into debt and harrowing one another to death translate successfully to the aftermath of the First World War? Only, perhaps, as edgy semi-farce, towards which Katie Mitchell's nervy, twilit production sometimes veers, not often intentionally. Acting to make you half believe in impossible characters might have saved it. But here you spend less time focusing on the poor puppets who flap around Mitchell's claustrophobic world than looking at the handsome, haunting set.