The fact that the Judge appoints Atticus Finch as the public defender tells us that the Judge is as fair as he can be in the system in which he works.  He knows that there is no way that an all white jury is going to found a black man innocent but he also knows that by appointing Atticus Finch, he is giving the black man the best chance he has.  If he were to appoint someone else, the defender might take the case but argue it half-heartedly because he would expect to lose.  Atticus Finch wants to win and does everything he can to win.

Although a minor character in the novel, the role he plays is a significant one as he is a counter balance to the overwhelmingly white racist south which is presented.  Were it not for the Judge, Atticus would stand alone as a non-racist.  At least in the novel, we have one more character who is concerned with upholding the law.