Richard Bean has had a busy year, and it isn’t over yet. Great Britain, his bawdy play about press ethics and police corruption, is transferring to the West End after hitting the spot at the National. Pitcairn, a new piece about the aftermath of the mutiny on the Bounty, will shortly arrive at the Globe after turning heads at the Chichester Theatre. And Made in Dagenham, a musical version of the 2010 film for which Bean has provided the book, looks likely to be one of the West End highlights of the autumn.

Here's a fun fact: this year the Merriam-Webster dictionary added a new definition for the noun "catfish". As well as the amphibian, a catfish now also refers to "a person who sets up a false personal profile on a social networking site for fraudulent or deceptive purposes." Having been popularised by the 2010 American film documentary of the same name, the term is also used casually as a verb, meaning to fool someone online.

This has been a busy season for Off Broadway musicals crossing the pond to London, from Dessa Rose and Dogfight to Forbidden Broadway and See Rock City. But for simplicity of approach coupled with swiftness of emotional attack, Benjamin Scheuer's solo musical The Lion stands apart. That's not just because the Anglo-American Scheuer, 32, possesses an apparent sweetness that makes his sungthrough embrace of anger, rage, and grief - all in the service, it should be added, of forgiveness and acceptance - that much more surprising.

Shared yearning for a place to belong is not a revelatory concept, nor is it given new dimension in this gently saccharine piece, yet although the whistle-stop tour only covers familiar landmarks, the journey is a convivial one. Adam Mathias and Brad Alexander’s pop/rock-cum-contemporary Broadway show meanders through six vignettes – with a loose thematic thread – that take place at American tourist attractions; some are all too brief, others outstay their welcome.

It is no mean feat to turn an audience against idealistic, painfully young marines heading for the nightmarish hell of Vietnam, but Dogfight comes perilously close to achieving that undesirable goal in the manner of their introduction. The band of brothers have just one night of freedom in San Francisco before deployment, and how do they wish to spend it? Competing to see which of them can recruit the least attractive date in a so-called "dogfight", with the winner – if there can really be a winner in such a contest – pocketing a wad of cash. On the Town it is not.

If comedy is tragedy plus time, either too much has elapsed since the fictional events of Jezebel, or not quite enough. Newcomer Mark Cantan's uneven screwball comedy pitting a methodical couple against a scatter-brained opposite with wacky misunderstandings aplenty, lacks the emotional heft to be more than genially inconsequential. And it's too enamoured of the old-fashioned TV sitcoms it references to subvert rather than merely replicate their well-worn tropes.

Cuckooed, Traverse Theatre *****

Mark Thomas's new show is in the theatre section of the Fringe brochure, but this hour, full of laughs and witty lines as it is, could easily be under the heading of comedy. Indeed, Thomas once made his living as a stand-up, even if his career has long defied any pigeonholing; professional irritant, activist and satirist are just a few job titles that could apply.

Rona Munro's history cycle may take some liberties with the facts, as the writer admits in the programme notes, but its broad narrative sweep has been talked about as a state-of-the-Scottish-nation trilogy. It's the first joint production of the National Theatre of Scotland and the National Theatre and the timing of its premiere at the Edinburgh International Festival couldn't be more pertinent – just a few weeks before Scotland votes on 18 September in the independence referendum.

“We are all in the gutter, but some of us are looking at the stars,” declares Lord Darlington in Act II of Oscar Wilde’s Lady Windermere’s Fan. He’s the classic Wildean cad - unprincipled, facetiously witty and in this production, possessed of the vilest pencil moustache, and yet the playwright gives him the most memorable line of the whole play. Why? To demonstrate that nobody is too completely good or bad not to be redeemed by beauty.

For those who have spent the past few months nodding along to World War I conversations while desperately trying to remember who killed that archduke and why, Rolf Hochhuth has kindly supplied a solution in the form of a dramatised European history lesson, making its English-language premiere at the Finborough.