The title spoofs What Price Beauty? (1925), a silent film featuring Rudolph Valentino's second wife, Natacha Rambova.
The railroad car in the background has the name Onion Pacific on the side, which is a take on the real Union Pacific railroad.
Among the items the dog uses to deflea himself is a bar of Lice Boy soap, a spoof of Life Buoy Soap, popular at the time. And the bathroom used sports the very latest in modern furnishings.
The brief playing of the Wedding March when Homer introduces his wife to his faithful pal was required by the censors at the time, otherwise the parade of flea children could not have been shown. Even cartoons characters had to abide by censorship standards back then.