The trouble is at the core with David Tennant (aka the Tenth Doctor Who) as the Prince. Even here, it's not for lack of trying. Tennant can get his mouth around a Shakespearean line, which is no mean feat. He gambols and prances about the stage enough to convince us that he is, if not mad, then at least running over with adolescent energy. Sometimes this works: when he berates Ophelia or Gertrude, or when he taunts Polonius, we can recognize him as just the sort of oversized infant that we'd like to pitch out of the house.
But if this is all we get from Hamlet, then it isn't a very interesting play. What really engages us is that this raw adolescent also has the seeds of majesty in him. Ophelia loves him because he is worth loving, and feels his loss so bitterly because he is worth the keeping. Denmark needs him, and we can feel Denmark's misfortune when it no longer has him. Tennant (or his director, Kenneth Doran) doesn't seem to get this. Tennant's Hamlet is at best no more than an engaging child. His death is pathetic, but doesn't come close to tragedy.
[An added complication is that Tennant himself is well into middle age. Hamlet's age is in any event a textual problem: is he 17 or 30? best to leave it as a puzzle and recognize that Hamlet may be both at once. But a middle-aged Hamlet who acts like a child--that much is only creepy.]
So hobbled, it's not surprising that the ensemble simply isn't equal to what must be one of the greatest scenes in all of Shakespeare: the prequel to the great sword fight, when Hamlet comes to accept his fate with a quiet dignity. Tennant mouths his way through the lines well enough, but it's perfunctory: nobody seems to have his heart in it. In particular, nothing in the prior development of the character leads us to accept Tennant as projecting the poise and comprehension that Shakespeare thought he could display.
As I suggest, this is a pity. With so many of the little bits right, and with a lead player in possession of such impressive technical skill, it's a shame to see it all go to waste. But if the the best they can offer is a technically more proficient Jude Law, it seems to me that they've thrown away a great opportunity.
Afterthought Evidently mine is not a universal view; cf. link, link, link.