According to Reinhold Weege on the Season 1 DVD commentary, the story Harry tells about how he got appointed judge is a true story. According to Reinhold Weege, the mayor of Los Angeles was so angry that he lost his re-election bid that he decided to hurt the new mayor, whom he personally hated, by filling all of the judicial openings with unqualified or under qualified personnel. At the beginning of the pilot, court clerk Lana Wagner (Karen Austin) even mentions that she doesn't know anything about "Judge Stone" because the mayor filled all the vacancies at the last minute.
Towards the end of the episode, Dan asks, "How did you get appointed to the bench?" Harry actually says, it was the governor's last day in office but was dubbed to the mayor's last day in office. You can clearly see his lips say governor's.