Green-Eyed Monster: The Professor often notes (to the point of it being a catchphrase) that Satan torments humans because he wants to bring everyone down to his level- he hates himself and his situation and wants everyone to be as miserable as he is. For extra points, Satan is actually described as having green eyes.
Wouldn't Hurt a Child: Satan has strict standards of not possessing anyone who isn't old enough to make moral choices, and is thus in one episode is shown to be enraged at fundamentalists who believe a child is possessed by him, and want to beat Satan out of the child.
The Atoner: Averted. The Professor, and then Scumspawn, spends a lot of time trying to reform Thomas. He doesn't really get it.
Flanderization: To an extent. In the first series, he's more of a malevolent cad, but later episodes present him as a rage-filled psychopath. Weirdly, this happens at the same time as efforts are made to reform him.