It's a kind of twisted and unfortunate compliment to media SF that the BBC breaks a decade or two's avoidance of Shakespeare in order to make a filmed version of an RSC production of Hamlet that happens to feature the Doctor as the prince and Captain Picard doubling Claudius and the ghost. But let's not be grudging; it was three hours of good, punchy, classic drama. David Tennant did actually bring some of the tics that he's been using to make people like his Doctor to his starring role; all that nervous, eccentric intelligence, the worry in those staring eyes, the bursts of energy and introspection - it was a perfectly respectable Hamlet while also being the David Tennant that the Who-fans will have wanted to see. Patrick Stewart, meanwhile, simply applied the intelligence and gravitas and charisma that he can wheel out for any role you care to pay him for to both purposes; why the director wanted him in both roles was unclear to me - I assume it was simply that if you've got one of the best mature actors of his generation available for this play, you might as well make maximum use of your resources. The ghost isn't much of a character, of course, but Stewart had some fun with Claudius's increasing but never quite adequate attempts at murderous deviousness.
(Hmm. Maybe... If the ghost is partially - though not completely - a projection of Hamlet's neuroses, and given that Hamlet doesn't seem to have seen much of his father for some years or to have had much in common with him, perhaps the face and voice he perceives could indeed be drawn from the available alpha male on whom he's projecting his Oedipal anger? Oh, heck, maybe maybe maybe - but that's making excuses, not adding anything to the play.)
Anyway, it would be wrong to imply that this was purely a two-star vehicle. The RSC cast was as good as you could expect, including Oliver Ford Davies as a Polonius so annoying that most of the audience will have wanted to stab him in the arras by "to thine own self be true" (though he actually took a bullet through a mirror in this incarnation); Edward Bennett struck me as a bit too Wodehousean as Laertes, but perhaps that was the point, while Mariah Gale worked to convey the underlying fragility in an Ophelia who initially seemed quite smart and sensible, before rather rapidly flipping under stress, and Penny Downie was a hard-drinking satin-dressed mature jazz siren of a Gertrude.
"Wodehousean", by the way, wasn't a big problem given that this was a more-or-less modern dress production, looking kind of 1930s formal in the early scenes where smart suits, ties, and court decorations were everywhere, before the more modern leather jackets and such began to intrude. (Hamlet carrying a medieval sword to threaten his friends with in early scenes just looked clunky, though; the large flick knife that he didn't quite use on the praying Claudius was more in keeping.) The production design was fabulous - all polished black marble, huge mirrors, and chandeliers; Elsinore had clearly acquired a great interior designer from somewhere, even if the battlements were still cold and drafty places for trench-coated sentries to pace in the vaguely defined wee small hours. The minor obsession with surveillance cameras initially looked more trendy than apposite (and not very '30s), but it became clear that Hamlet was partly being driven to distraction by the sense that he was perpetually under observation, which was why he grabbed a gun to shoot out that mirror and hence Polonius, so I'll give it a pass.
Overall, then, three hours of David Tennant, Patrick Stewart, and a lot of other top professionals doing their stuff to fine effect, shiny and crisp; the Beeb can have my license money for this, and will in any case doubtless make plenty on the DVD sales, and I don't think that the Who or Trek fans will have been disappointed.