A chalky-faced man stands in the shadows and his limbs jolt about, as if battling for position beneath his skin. This is the ghost of Hamlet's father and he is a fearful sight in ACS Random's Victorian and spectral take on Shakespeare's tragedy. When Hamlet senior's spirit croaks "Remember me!", it seems superfluous. This is a creature impossible to forget, even if this production's real-life characters aren't as vibrant as its figures from beyond the grave.

One of the oddities about theatre is that there can be a gripping performance at the heart of an underwhelming production – and so is the case with Maxine Peake’s Hamlet, directed by Sarah Frankcom. This was a much anticipated production – Peake going home, as it were. She started acting at the Royal Exchange Youth Group and is now an associate artist at the theatre, and has recently been seen giving a towering performance in The Village on BBC One.

Is that a sabre you see before you? It could be if you’re talking any of multiple stage and screen versions of Hamlet, the Shakespeare play that puts centre-stage arguably the most esoteric of all Olympics activities: fencing. (Well, OK, beach volleyball is possibly just as rarefied, though it’s hard to imagine Hamlet and Laertes having much truck with that.)

We’re fresh out of superlatives. The Globe to Globe season has put a girdle around the earth in 37 languages, and the visiting companies have now left the building. You have to high-five the Globe’s chutzpah for mounting this wondrous contribution to London 2012’s World Shakespeare Festival in the first place. But in quite properly keeping the biggest till last, it surely took extra testicles to stage the famous play about a royal family in turmoil on this of all weekends.

First come the strip-lit corridors, the stained breeze blocks, the locked doors; later there are restraints, drugs, needles. The time is out of joint, and we are all imprisoned in a nightmare of confusion, paranoia, guilt and despair. Who are the mad? Who the sane? In Ian Rickson’s thrilling production of Shakespeare’s great tragedy, it’s often frighteningly unclear.

Lightning hasn't quite struck twice at the Theatre Royal Haymarket, where Trevor Nunn's dazzling reclamation of early Terence Rattigan (Flare Path) has been followed by the same director's transfer from Chichester of Rosencrantz and Guildenstern Are Dead, Tom Stoppard's first play. How does this 1966 gloss on Hamlet by way of Beckett hold up today? Engagingly enough, not least when its two tireless leads are in full existentialist flow. But some may nonetheless feel a degree of exhaustion, however much they'll want to cheer Samuel Barnett and Jamie Parker on.

Derek Jacobi (b 1938) grew up in Leytonstone. His father was a tobacconist, his mother worked in a department store. Although he entered the profession in the great age of social mobility in the early 1960s, no one could have predicted that he would go on to play so many English kings - Edward II, a couple of Henry VIIIs and Shakespeare’s two Richards - as well as a Spanish one in Don Carlos. This month he prepares to play another king of Albion: Lear, against which all classical actors past a certain age must finally measure themselves.

The relationship between stage and screen has always been fraught with antagonism and suspicion. One working in two dimensions, the other in three, they don't speak the same visual language. But recent events have helped to eat away at the status quo. On the one hand, theatre has grown increasingly intrigued by the design properties of film. Flat screens have popped up all over the place, notably in Katie Mitchell’s National shows and at the more ambitious work of the ENO. Meanwhile, theatre and opera have been encouraging those who, for reasons of distance or price, can’t make it to the show itself to catch it on a cinema screen instead.

The National Theatre’s new production of Hamlet is both a very good Hamlet, yet also a somehow disappointing one. For a work so rich in possibilities, with so much emotion, so much superb and intricate engineering, it is often like this, in England or anywhere else - inspiring and unconvincing at once.

It's an axiom trotted out in the acting profession that a young male actor measures himself against the role of Hamlet, much as an older one does with Lear. It's been announced this week that a couple more are having a stab at the Prince of Denmark. Michael Sheen will be the Young Vic's Dane in winter 2011, while Sheffield will see John Simm's this autumn. And we already know that the next tranche of Hamlets will also include Rory Kinnear at the National later this year