I'd put off viewing this version of "Hamlet" for a long time, because I'd heard that they'd turned this most cerebral of plays into an "action movie", but I ended up quite liking it.
I should begin by saying that I approve of ALL interpretations, because each choice reflects different possibilities all of which are supportable by the text; no one vision can encompass every potentiality inherent in the play. And the text per se, of course, will always exist in absolute form despite the number of hands that manipulate it.
All productions (except Branagh's) cut certain elements as a sacrifice to tighter (though narrower) focus. And the use of film rather than stage allows (even necessitates) different types of dramatic development. Films unfold at a different pace than stage plays. Zefirelli's adaptations WORK as film-making, without detracting from (or unnecessarily supplementing) Shakespeare's language. For instance, the little "prologue" scene showing the internment of the dead king. It is original to the movie, and yet the dialogue is still from the play; it doesn't misrepresent anything about the characters in its new context. And perhaps most importantly, it "works" in the movie that the director is making. But on to the substantive comment...
Mel Gibson was, in my opinion, too old to be Hamlet (making Glenn Close, by extension, too young to be Gertrude), but the issue of Hamlet's age has always been a problem. He's 30 in the text (this version leaves out that calculation), but that makes some of his relationships (with Ophelia, for instance) seem a little... immature. And yet if he's portrayed too young, his depth of thought is almost impossibly precocious. But I thought he was convincing nonetheless, particularly in expressing something that I've found central to my understanding of the play but I all too rarely see dealt with in Hamlet's portrayal, which is this:
Hamlet IS quite mad. 'Tis true: 'tis true 'tis pity, and pity 'tis 'tis true. From his first meeting with the ghost onwards, he is profoundly disturbed. It is irony that he then puts an 'antic disposition' on, because he has in actuality gone quite 'round the bend.
Mel Gibson not only gives the first convincing portrayal of Hamlet's "pretended" madness that I've seen, but he also shows us the desperation of the character in his quiet moments. Hamlet is not, as Olivier posited in his 1948 version, merely "a man who could not make up his mind." Gibson's Hamlet spends much of the film alternating between mania-induced impulsiveness and paralyzing inability to act. The Dane is not merely melancholy, he is certifiably manic-depressive. (Claudius, I believe, sees this.)
Over all, I believe that this would be a good introduction to the story of Hamlet for those who otherwise would have had no contact with it, although as I said it can then be supplemented by other adaptations (and of course there's no substitute for, ultimately, reading the text).