The year is 1957, and Sputnik has just breathtakingly launched into space as Franklin, a fledgling American composer, gazes up at the stars and jubilantly welcomes the dawning of a new age, when anything will be achievable and his generation will, he believes, realise its dreams. It's an uplifting scene from an uplifting-sounding musical, Merrily We Roll Along.
Sondheim's title is ironic, however, for Merrily reverses through time, to conclude in 1957, like a regretful memory play. We start spooling back from 1980, when Franklin has scored Broadway hits and turned into a Hollywood big shot, only with a nagging awareness that he has sold out and lost his true soulmates – his devoted writer-friends Charley and Mary.
It seems hard to believe – though, granted, it isn't flawless – that Merrily bombed when first staged in the US. The journey towards a sad yet simultaneously happy ending is cleverly engineered, as is the counterbalancing of sentiment with satirical digs at the tosh-touting end of the entertainment industry.
Maria Friedman's revival, her debut as a director, proves terrifically assured. It is technically polished, with retro chic, remarkably fluid scene changes on a long, narrow stage, and perfectly gauged amplification. This means you can enjoy the Menier's intimacy without the brassier numbers jangling the nerves.
What's really outstanding is the emotional sincerity and minutely detailed naturalistic acting integrated with the songs: Damian Humbley makes Charley's patter song "Franklin Shepard, Inc" both funny and infuriated, while, contrastingly, Mark Umbers wraps his arms round Jenna Russell's Mary with a platonic tenderness that's breaking her heart.
And, in news elsewhere, Boris is now in charge. He's running the country. In fact (good grief!), he's agreed to be crowned, allegedly due to popular demand. Beware, though. Anyone supporting the opposition movement may be interrogated and tortured, or keel over without any decent medical explanation.
The setting for all this, I should explain, is Russia circa 1600. As part of its A World Elsewhere season – staging foreign classics that tie in with Shakespeare's era – the RSC presents Pushkin's history play Boris Godunov (the source of Mussorgsky's opera of the same name).
Written in 1825 and censored by the authorities at the time, Pushkin's saga of political machination portrays the titular tsar as the covert murderer of the rightful heir to the throne, the princeling Dmitry. By way of a belated comeuppance, Boris is confronted by a pretender – a young monk-turned-warmonger, Grigory – who claims to be Dmitry, mysteriously back from the dead.
This production glisters beautifully, designed by Tom Piper and directed by Michael Boyd (who has just bowed out as the RSC's artistic director while, manifestly, keeping a foot in the door). It is staged on the Swan's thrust stage, against a backdrop of golden ladders and balconies. Fur-trimmed robes swing underneath, on hangers. This is a realm of deceptive masquerades and rapacious aspirations.
Adrian Mitchell's blank-verse translation, not poetically florid, makes the sprawling, episodic storyline seem fleet. The plot also echoes Shakespeare's Richard III, Macbeth and Henry IV, Pushkin having been inspired by the Bard. That said, the cast fails to pull off a tavern scene's sudden switch into comic rhyming couplets.
More crucially, Lloyd Hutchinson's Boris isn't gripping. His salt-of-the-earth manner, chattily addressing the audience in his soliloquies, needs to be either veined with greater menace or more guilt-ravaged. There are moments of swirling physical theatre, as ceremonial processions give way to ballroom waltzes then battlefields, with greatcoats spun like flails – accompanied by wild Slavic violins, drums and ethereal choiring (excellent score by John Woolf). Playing Grigory, newcomer Gethin Antony displays fiery ambition. Yet the acting feels skin-deep, a gilded show of passion.
James Tucker is more intriguing as the discontented aristocrat Shuisky, playing a game of realpolitik as Adam Burton's Semyon lurks in the shadows – a secret policeman in a priest's robes. The layered costumes, with cloaks increasingly cast off to reveal modern-day suits, also pointedly suggest that, in spite of passing centuries and revolutionary upheavals, nothing changes.
Kiss Me, Kate's Old Vic transfer from the Chichester Festival, directed by Trevor Nunn, is somewhat hit and miss. Cole Porter's comic musical from the 1940s offers a string of fabulously catchy numbers, while we watch Lilli and Fred – a stroppy showbiz diva and her ex – escalating their squabbles onstage as they perform The Taming of the Shrew in provincial Baltimore. Indeed, the dazzling high-quality singing may well blow you away, with Hannah Waddingham and Alex Bourne waxing almost operatic in the leading roles (under musical director Gareth Valentine). I greatly warmed to this show after the interval, the second half kicking off with the slinky jazz number "Too Darn Hot", choreographed by Stephen Mear.
Nonetheless, hearing the songs without Sam and Bella Spewack's book might have been preferable. Many of the Taming scenes are underdirected, with hammy buffoonery from Bourne and others, which is presumably meant to be a send-up of the C-rate but merely falls flat. This Kiss Me, Kate is no match for the Old Vic's previous play-within-a-play farce, Michael Frayn's Noises Off. There were, indeed, moments when I was so bored by Nunn's inanely grinning chorus girls, that I was tempted to turn termagant myself and fling some punches.
'Boris Godunov' (0844-800 1110) to 30 Mar; 'Merrily We Roll Along' (020-7378 1713) to 23 Feb; 'Kiss Me, Kate' (0844-871 7628) to 2 Mar
Mark Rylance is charmingly funny as Olivia in the all-male Twelfth Night at the Apollo, Shaftesbury Avenue (to 9 Feb). A heartbreaking bio-drama, The Dark Earth and the Light Sky, at London's Almeida (to 12 Jan), asks whether Edward Thomas (Pip Carter) is less devoted to his wife (Hattie Morahan) than to his fellow poet Robert Frost.