I can see why Burton wanted the tape destroyed
Supposedly, this performance was taped once and broadcast, and Richard Burton requested that the tapes be destroyed afterwards. I can see why - it was a simply terrible production with bad performances all around.
Burton himself is probably the biggest disappointment, because I expected so much from his performance. He acts as though he's a) drunk and b) doesn't really give a damn, hoping that his voice and star power will carry him through as he shouts his way through the production. At some level he's thrilling to listen to, but as many have noted, he gives recitation, not acting.
Hume Cronyn was the only member of the supporting cast who gave a memorable performance. He really played to the audience, but that's fine in a stage production. Cronyn made Polonius very funny, as he's supposed to be. The rest of the actors and actresses involved seem to have no idea of what to do with the material. Whoever played Laertes was memorably bad, and Alfred Drake brought nothing to what should have been the most important role in the play after Hamlet's.
And to top it all off, the audio and visual quality is poor. Surely they had better recording technology in 1964!