You can get a full idea of how the play played out at MG's site.
Let me just say that they made brilliant use of light and dark - a shiny black floor which the soldiers shone their Mulder-and-Scully torches on, which reflected back onto each other's faces. The rear wall mirrors that cracked to amazing effect. A brilliantly doddery Polonious, played by Star Wars favourite Oliver Ford Davies (Sio Bibble), a great to see Patrick Stewart (who almost laughed when, during the interrogation of Hamlet to ascertain the location of Polonious's body, Tennant opts to reply with the same deep, Stewartesque tones "He's in Heaven!").
Tennant is, as they say, a good Hamlet. Fully realised, brilliantly unhinged at times, funny and distraught - but, as the lady on the front counter said to us, it's not dark enough.
There was perhaps, too much humour. And while, as Laura pointed out, Shakespeare purposefully added comedy into his tragedy and tragedy into his comedy, Hamlet needs to be a far more brooding piece than it was.
Not that it ruined the enjoyment - certainly, Tennant's choices made for a more relatable Hamlet than, say, the knowing-Hamlet of Brannagh's (though we have just bought a copy of Brannagh's Hamlet because it's great).
Anhyoo, here's a piccy of David Tennant signing autographs - and yes, we were sad enough to join in, though we failed to get one.