In his last minutes as the artistic director of Shakespeare’s Globe, Dominic Dromgoole took to the stage to reflect on his years at the helm. Behind him was the cast of Hamlet, home after two years on the road playing to audiences from every country on the planet. He acknowledged his predecessor Mark Rylance, who waved a hat from the throng of groundlings, and then pointed up to the circle where his successor Emma Rice was greeted with gales of welcoming applause.

There’s something endlessly fascinating about T E Lawrence. In popular culture, he has been immortalised by Peter O’Toole’s dazzlingly blue-eyed performance in David Lean’s Lawrence of Arabia, but is there more to this English eccentric than freedom fighting on the side of the Arab Revolt against the Ottoman Turks? Howard Brenton certainly thinks so, and his portrait of this strange, curiously unworldly and painfully conflicted character is, like its hero, full of great potential, much of which it fails to realise.

In this 400th anniversary year, amid what feels like 400 million shows and tributes, it’s increasingly difficult for a Shakespeare production to stand out. No such problem for Emma Rice’s opening salvo, which responds to those critical of her appointment in resolute fashion. Never thought you’d see fireman’s poles, amplification, Indian sitar and disco lights at the Globe? Think again.

If Downton Abbey creator Julian Fellowes were (a lot) more like Ibsen, our national viewing habits would be in good hands. But then, as the hero of An Enemy of the People discovers, presuming to know what’s good for the public is a dangerous game. In his first full stage role in 12 years, the Earl of Grantham, AKA Hugh Bonneville, returns to his local Chichester Festival Theatre as a whistleblower who thinks he’s doing his town a favour.

You rarely see a full production of Shakespeare's dream play so magical it brings tears to the eyes. But then you don't often get 42 players and 14 voices joining the cast to adorn the text with Mendelssohn's bewitching incidental music, plus the Overture composed 16 years earlier – certainly the most perfect masterpiece ever written by a 17-year-old.

And so, it’s farewell to Mark Thomson with his final production as artistic director of Edinburgh’s Lyceum Theatre, after 13 years in the job (incoming artistic director David Grieg unveils his new season next week). With Homer’s The Iliad, in a new dramatisation by Clydebank-born playwright Chris Hannan, Thomson is going out with a bang – it’s a big, bold show that tackles one of our culture-defining myths, albeit a lesser-known one (‘the greatest story never told" is how the goddess Hera describes it within the play itself).

Playwright Nick Payne has carved out a distinctive dramatic territory – neuroscience. In his big 2012 hit, Constellations, he explored the effect on memory of living with a brain tumour, while two years later in Incognito, the story of what happened to Albert Einstein’s brain was married to the case of a man who had parts of his grey matter removed to cure his epileptic seizures.

Smoking weed on the Orient Express. Drinking at a brothel in Paris. Tricking the military police in Istanbul. Smuggling a Da Vinci into Paraguay. As travel itineraries go, it’s certainly no Saga break. But then Graham Greene’s Augusta is no ordinary literary aunt. The antidote to Oscar Wilde’s Augusta Bracknell, Greene’s 75-year-old heroine is a lusty free spirit who terrorises Victorian values and turns her nose up at the law.

The Cotton Blossom looks mighty fine in its latest London iteration, Daniel Evans's winning Sheffield Theatre revival of Show Boat joining the ongoing runs of Guys and Dolls and Funny Girl to offer West End audiences a synoptic view of Broadway musical history. And surely no Broadway title remains more iconic than this one – the 1927 collaboration between Oscar Hammerstein II and Jerome Kern that set the musical form on course towards a level of maturity and daring that few up until that time would have thought possible.

Blood, sexual violence, power games and lashings of nudity. Not Game of Thrones, whose new season has just premiered (yes, he’s really dead. Well, for now) – and whose shadow Kit Harington is trying to escape – but Jamie Lloyd’s graphic take on Marlowe. It’s a production determined to hold your attention, and, thanks to its comic carnival of excess, largely successful in that pursuit. However, like the magic tricks bestowed on its soul-selling protagonist, it’s rather more flash than substance.