The little girl Tonya is a reference to Tonya Harding, who was involved in the attack on her competitor Nancy Kerrigan. Kerrigan received an injury to her knee before a skating competition.
During the discussion of the nose surgery, the Professor says, "Listen to Orange Joe," a reference to an earlier episode where Fry states, "Most people just call me Orange Joe."
The bug bomb brand used to fumigate Zoidberg's dumpster is "Hal's Roach Bombs", the tagline being "Kill The Little Rascals". This references filmmaker Hal Roach, as well as his Little Rascals series of shorts.
Marianne's flower stand is The Flowering Inferno, a reference to the disaster film The Towering Inferno.