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.
Hypocrite: One of the main reasons for his hatred of humans is their refusal to own up to their mistakes, yet he continually objects to any attempt to blame him for his own rebellion against God and subsequent banishment from Heaven.
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.
Never My Fault: After marrying Edith's daughter, he tormented her to the point of insanity. He eventually accepts 3% of the responsibility for the marriage's failure, which Scumspawn notes is 3% more than last time.
Shrouded in Myth: She's absolutely nothing like you'd expect from her work, or even from historical accounts.
Never My Fault: He maintains that the Holocaust was merely overreacting to being filmed in the shower, and he blames his failed invasion of Russia on Jesse Owens.
Ultimate Evil: He's the most frequently mentioned out of all the historical figures, but he never speaks, is never spoken to, and other than one scene where he is explicitly in disguise, is never even spoken about in such a way that one can infer his presence.