The answer to the Mathemagician is "413.2857142857143".
Lisa is right when she points out to the Mathemagician that 7 goes 4 times in 28. She could have also added that 7 times 3 is 21, not 22 as he writes it on the blackboard... But hey, "magic seven"!
As almost everyone at the party was taken to the hospital, the party was over, so Lisa could have left without pretending to be sick or being rude.
In Principal Skinner's office, a picture of Springfield Elementary is on the wall where it is colored purple. This is presumably a reference to the school's appearance in Season 1 (as well as some stock pictures reused in Seasons 2, 3, and 4).
Skinner is 44 years old, as mentioned when Chalmers says that it is clear Skinner and Krabappel have been falsely accused because no one would pretend to be a 44 year old virgin.
Mrs. Krabappel's name on the envelope is misspelled as "Enda" when Bart is opening and reading the letter, but is spelled correctly when viewed in closeup.
Nelson kept rejecting Martin’s invitation to his birthday party, but he still attended. He was likely bored that weekend, as was the case with Bart and Milhouse, or he may have intended to beat up Martin or some other nerd there.
The Mathemagician, whom Martin hires for his party, is modeled after Bill Gates.
Bart saying "Set your faces to stunned" is a reference to the Star Trek catchphrase "Set your phasers to stun".