The "fight" between Bart and Lisa at the end of the episode is an homage to the "fight" between Rocky and Apollo at the end of Rocky III.
This is the second time Marge protests against violence the first being "Itchy and Scratchy and Marge" when she protested against Itchy and Scratchy due to cartoon violence.
The UPKCC is a parody of UFC and it's promoter Chet Englibrick is a parody of Dana White.