In To Kill a Mockingbird, what is Judge Taylor's attitude toward his job?

Judge Taylor in Lee's To Kill A Mockingbird takes his job seriously. He is the only judge in a racist community when a very controversial case crosses his desk. Rather than play to the white majority's wishes to convict Tom Robinson without much of trial, Judge Taylor appoints the best lawyer in the county to defend a black man. He knows Atticus Finch will provide the best possible defense for Tom Robinson even though the community might hate him for it. He does this because he believes everyone deserves a fair trial. The book doesn't come out and say these things explicitly, though. Most of this can be inferred by what Atticus says to his brother about his appointment as follows:

"Before I'm through, I intend to jar the jury a bit—I think we'll have a reasonable chance on appeal, though. I really can't tell at this state, Jack. You know, I'd hoped to get through life without a case of this kind, but John Taylor pointed at me and said, 'You're It'" (88).

Atticus's enthusiasm for justice is exactly why Judge Taylor tells him "You're It." He knows Tom Robinson has a chance with such a good lawyer. By providing Tom with a good lawyer, Judge Taylor shows he is not a part of the racist majority of Maycomb.
On the other hand, Scout points out that Judge Taylor runs his courtroom "with an alarming informality" (165). She says Judge Taylor often looks sleepy, puts his feet up on the desk, and has been seen cleaning his fingernails with a pocketknife! Although he may seem disconnected or disinterested while sitting on the bench, Scout says the following about Judge Taylor's attitude:

He was a man learned in the law, and although he seemed to take his job casually, in reality he kept a firm grip on any proceedings that came before him (165).

Therefore, Judge Taylor's attitude towards his job may seem relaxed on the surface, but ultimately, he has more control over what is going on in his courtroom than it appears.