This newly-restored version of one of MGM's most hallowed musicals is making the seasonal rounds with a run at the BFI and selected cinemas around the country. Directed by Joseph L Mankiewicz in 1955, the piece drips with period charm, while its pairing of Marlon Brando and Frank Sinatra is still capable of generating a box office buzz 60 years later. But (I'll just whisper this) it may seem like a bit of a slog for modern audiences.

To do Mamet’s work justice, you must be able to deliver dialogue with the speed, skill and breathtaking bravura confidence of Usain Bolt. In Lindsay Posner’s much-hyped but frustratingly sluggish revival at the Playhouse Theatre, only one of three cast members rises to that challenge – and it’s the one who’s generated by far the fewest column inches. British actor Nigel Lindsay is the breakout star of a strange experiment in meta-satire, in which Mamet’s denunciation of a movie-going public allowing crass commercialism to override creative integrity gains surreal significance.

“We are not politicians – we are artists.” It’s the familiar cry of creatives all around the world, but it came with an added, rather surprising accent when uttered by Moscow International Film Festival (MIFF) president Nikita Mikhalkov at the event’s closing ceremony.

As Benedict Cumberbatch's Sherlock reached the end of its latest brief span, Timeshift [****] surveyed the history of dramatic interpretations of Baker Street's finest with a wry eye, in a narrative sprinkled with nutritious facts and anecdotes.

They called Rita Moreno the triple threat – she could dance, act and sing. But even her spirited performance as Anita in West Side Story could not satisfy United Artists: the doomy low notes of "A Boy Like That" were considered out of her range, and the number was ghosted by Betty Wand, one of the scores of unknown singers who rescued on-stage stars from ignominy.

BBC Four’s new series Sound of Cinema: The Music that Made the Movies is shocking. The overwhelming majority of arts-based TV consists of programmes consigning specialist knowledge/presenters to the sidelines in favour of dumbed-down, easily digestible generalisations mouthed by all-purpose TV-friendly faces. But this three-part series is fronted by, gasp, a composer who uses insider knowledge to hook and hold the viewers.

You might wonder if anybody really deserves three and a half hours of TV biography, but after the first half of Robert Weide's immense survey of Woody Allen, the nebbish messiah, I was pawing the carpet in anticipation of part two. Documentaries don't, as a rule, leave you in seizures of mirth, but the judicious selections from Allen's bottomless catalogue carried a sealed-in guarantee of hilarity despite being snatched from their original context.

If Mae West was once described as a plumber’s idea of Cleopatra, Elizabeth Taylor, clad in gold and covered in real diamonds, is Hollywood’s ideal in Cleopatra (1963). Sumptuously restored to 2K DCPs and rereleased on the big screen, Taylor’s beauty and the chemistry with future husband Richard Burton remain throbbingly alive - in a production so mired and luckless that it tried to spend its way out of trouble.

With its story of youthful love entrapped by fate, Tabu relishes the glorious primal energy of the South Seas, which was where German director FW Murnau, best known now for his expressionist Nosferatu, but then recently established in Hollywood and acclaimed for the likes of Sunrise, found himself in 1929.

Mrs Thatcher famously presided over a huge rise in unemployment, but down the years she kept a large sorority of impersonators (and one male one) off the dole. She was lucky with her mimics, who included some of the great actresses of the age, and never luckier than when Meryl Streep (pictured below) inhabited the role of Britain's first female Prime Minister. To her three election victories, Thatcher was able to add - if by proxy - an Academy Award for Best Actress.