Besides bearing the derogatory term for "cops", most likely because the head coach is Chief Wiggum, Bart's team name, the Mighty Pigs, is a parody of both the Disney film The Mighty Ducks, and the professional NHL team the Mighty Ducks of Anaheim, now called Anaheim Ducks.
Large sections of the episode are references to The Mighty Ducks film. Milhouse being tied to the goals could be a reference to the goalie being tied to the goals in training to teach him to not be scared of being hit.
Regarding the Kwik-E-Mart Gougers, to 'gouge' is not only a vicious act of violence but also the act of 'price gouging' when prices are spiked to a level that is considered unfair or exploitative.
The school auditorium was named the "Butthead Memorial Auditorium", a reference to the series Beavis and Butt-head.
The auditorium being named that, as well as Skinner's proverbially kicking himself afterwards upon making the announcement, was overall a reference to an incident in Greenwood, South Carolina, where various children voted to have their school named "Springfield Elementary School" after the eponymous location from The Simpsons as well as the resulting controversy. Ironically, in a press release by Fox News, Bart was stated to have said in response to the school's naming "At least it wasn't named Beavis and Butthead Elementary".
The Apple Newton was an early PDA device with a reputation for poor handwriting recognition.