Character Analysis
Arthur is Jack's real father, who Jack puts a lot of faith in and who constantly ends up letting him down. "We would all be together again, as we were meant to be." (31.14) Jack says at the very end, encapsulating all the wild hopes that he pins on his father. Who is never there. And doesn't send them money. And "took off for Las Vegas with his girlfriend" (31.1) the day after Jack arrives for a visit. So… not exactly a stable figure, even before he "had gone crazy and was now in the custody of the police." (31.3)
Jack's dad is probably most important for his absence. Since he's not around to be a real dad, Jack can put all of his Cool Dad fantasies on him without being disappointed (or at least not as disappointed as, say, Dwight makes him). That gives Mr. Wolff the ability to let him down again and again, since he's never there long enough to let the disappointment become permanent. Geez, he's almost a bigger jerk than Dwight!