It's a pretty good production. I saw it at Stratford --- sorry, no queuing, I just filled in my full member's form and received row C for my daughter and me by return of post --- and rather enjoyed it. It's been cut heavily to fit in three and a half hours, which is good --- compare Dear Ken's production in the early 90s, which was nearly an hour longer.
Tennant is surprisingly good --- remember, Hamlet is a young man's part, and his Doctor has been an audition for Hamlet from the off --- but Stewart steals the show as Claudius. He's old RSC, and can actually speak the verse, and that brings out of Maria Gayle as Ophelia (a name to watch: she did a great Miranda a couple of seasons ago and she's sensational here, and looks great in her bra and knickers too) and especially Penny Downie as Gertrude (again, old RSC: she played Lady Anne opposite Sher's Richard III amongst other things) fine, fine performance.
You won't come away having learnt something about Hamlet, either the man or the text, that you didn't know before, but you'll have laughed (a lot: it's _funny_, with Oliver Ford Davies as Polonius timed to perfection) and seen some great performances. The whole thing is slightly less than the sum of its parts, but it's a fine evening's theatre.
It won't be one of the great RSC things that's remembered for decades to come: my wife saw the Sher R3, we both saw the Stephens Lear and the Brannagh Hamlet and the Mendes/Russell-Beale R3 and the Juliet Stevenson Becket Shorts, I saw all eight of the Histories in four days over Easter.
But if you don't know the play it's a great introduction. I think the young might find it all a bit too angsty. My daughter, 12, isn't a Shakespeare neophyte --- to the amusement of people sat near us she was able to compare Patrick Stewart's Claudius with his Hamlet at Chichester and his Prospero in the old main house --- and she was happy to see Tennant, especially two feet away on the walkway. But she enjoyed the Macbeth more, the motivations being a lot clearer (and, to be honest, the production a lot better: Goold is a real rising star). And if you do know the play, it's light, it's fun, it's well acted, and at worst you'll be left with a slight feeling that there's more to be had from the text.