Theodore Bikel received his only Oscar nomination at the moment for portraying Sheriff Max Muller in The Defiant Ones.
Bikel really isn't asked to do very much in the role of the Sheriff. I suppose a southern accent maybe was wanted since he sort of tries to do one in just his first scene than proceeds to pretty much give up on it right afterwards. Other than that he just needs to be a rather kindly Sheriff which Bikel shows in a very relaxed fashion. He is anything but intense and I suppose he is properly humane I guess in his portrayal, as he makes the Sheriff just a nice guy.
The whole point of the performance and the character seemed really just to show the audience that if Poitier and Curtis will be captured they won't be mistreated by those chasing them. Bikel is technically just fine at doing this there is nothing wrong with his portrayal. There just is not much to it either, he is there does his piece every so often sets up the humanness of the man nothing more. He never takes your interest from the main story line but that was not the point of the Sheriff either. It is a satisfactory performance in a functional role no more no less.