The pleasures to be found in the pitfalls that are part of live performance rear their accident-prone head yet again in Peter Pan Goes Wrong, the latest exercise in controlled (or is it?) chaos from Mischief Theatre, the young and clearly very resilient troupe that is gradually extending its farcical tentacles across the West End.

The first surprise in the Traverse Theatre’s seasonal production comes on entering the theatre – being led backstage, then onto what’s normally the performing area, and finally to two ranks of audience seating either side of a gently undulating transverse strip of stage.

Widely hyped as “an Alice for the online generation”, and “a coming-of-age adventure that explores the blurred boundaries between our online and offline lives”, this version of Lewis Carroll’s Wonderland stories is advertised with a poster that shows a Cheshire cat whose smile is more drug-addled rictus than quizzical grin. On the other hand, the team behind the show features three creatives who should be working at the top of their game: Britpop legend and opera composer Damon Albarn, playwright and scriptwriter Moira Buffini and National Theatre supremo Rufus Norris.

A supposed Stoppardian footnote gets a first-class reclamation in Howard Davies's sizzling revival of Hapgood, the espionage-themed drama from 1988 that resonates intellectually and emotionally to a degree it didn't begin to achieve at a West End premiere that I recall almost three decades on.

Is Jim Broadbent Britain’s best-loved actor? The slate of screen roles he’s accumulated over the years – this Christmas Carol is his return to theatre after a decade away – has surely given him a very special quality in the nation's consciousness, a combination of general benignity with more than a hint of absent-mindedness, an almost madcap bafflement at the world.

North Korea is the kind of place that haunts the imagination of the West – and not in a good way. One of the last hardline Communist dictatorships, it is also a country of immense sadness, a landscape of food shortages and human-rights abuses. Yet its regime calls this dismal place the "Best Nation in the World". To us, it’s a secret world, a strange culture difficult to comprehend, easy to fear. Small wonder that, in American playwright Mia Chung’s 2012 play, two hungry sisters fantasise about leaving it for good.

There’s a happy, cyclical logic to this first production of Cymbeline – Shakespeare’s late tragicomedy of love and jealousy – at the Globe’s Sam Wanamaker Playhouse. The first play Shakespeare wrote for the candle-lit, indoor Blackfriars Playhouse, Cymbeline was quite literally made for this space. How disappointing, then, that director Sam Yates proves so wilfully blind to the theatre’s unique spatial and dramatic possibilities, delivering a production that might charitably be called faithful, but which more often feels simply blank.

Just what constitutes reasonable behaviour in an enlightened society? Not long ago, the death penalty fell under that umbrella in Britain, and state-sanctioned killing as punishment for the crime of, well, killing is just the kind of twisted irony that cries out for the Martin McDonagh treatment. Here it is, ending the playwright’s 10-year absence from the London stage, and his Royal Court hit fully earns its West End transfer.

Events have overtaken this Macbeth, dramatically heightening its queasy topicality. Not just brutal beheadings and torture, but the cost and collateral damage of conflict without end, and the scourge of a tyrant slaughtering his own people, strike one anew in the wake of recent debate. Carrie Cracknell’s interpretative, modern-dress production traps us in a military underground bunker, drained of light and colour – a Hell as acutely psychological as it is physical. Not for nothing does the doomed Macbeth fear the “diseased mind”.

One of the joys about this stage adaptation of Jules Verne’s Around the World in 80 Days is the contrast between its phlegmatic hero Phileas Fogg, who deals with everything in terms of precision and logic, and the picaresque confusion of his journey. Fogg (Robert Portal) has the habit of laying down portentous truths in an attempt to mediate the scampering mix-ups that he encounters at every stage. One such aperçu, “A well-used minimum suffices for anything,” serves nicely as a verdict on Lucy Bailey’s energetic, engaging production.