I up-voted this because of that very question, TeenerTot.
There's an interesting debate in Shakespearean scholarship about whether Othello ultimately makes more sense with an actor who's black, or a white in blackface.
To boil down the debate as far as I remember it:
-In order to emphasize the deliberate theatricality of Othello the play, with Iago as an evil artist, and with ironies about Othello's self-image you'd want to stage it with blackface, even unrealistic blackface.
(This might also help get at the oddities of racism in cosmopolitan societies)
In order to get at Othello the character's suffering humanity, and imagine him as a person worthy of both sympathy and antipathy (so to speak) you'd want stage it with an actor who's racially African (setting aside the North African question here). Race is one factor among many in the Othello-Desdemona-Iago-Venice tangle, and I don't know how you'd show this if everyone's looking at an impersonation the whole time.
Formalism vs Realism, to make it one-dimensional.
There's also the question of the intentions of Olivier and his production (as well as Olivier's artistic choices) which I imagine could go from just about one extreme to the other. It looks like the critics of 1965 were all over the board about it. That's a perfect year for either a progressive-if-bizarre sensitivity, or a ham-fisted obliviousness, or worse.