He calls himself a "fiscal conservative" and a "social liberal". The film says little about his terms in Congress from 1969-1977. Koch actually wrote one time that he supported the idea of filial responsibility, that adult children should be held responsible for their parents. (New York State, however, does not have a filial support law.)
Koch was felt to have an uneven record with African-Americans. He first supported and then tried to close a hospital in Harlem as part of New York's financial restructuring. He does refer to himself as "white" and his Jewish background, while shown (in extended family events) doesn't seem to put him in a a "minority".
I believe Koch was still in office when the police scandal associated with the Central Park Five occurred in 1989 (see Dec. 15, 2012 posting).
By the way, I do remember those old subway tokens of the 1970s. I was living in Dallas for most of the time if Koch's mayoralty; I left NYC in early 1979, when things were still not good.