Bart Simpson's act in the stupidity contest of eating anything the audience throws at him, is a possible reference to the Tim Burton film Beetlejuice. In that film Beetlejuice says during a commercial that he'll eat and swallow anything the potential client wants.
The quote, "Shut up-a your mouth!", almost sounded like Boris Badenov's catchphrase, "Sharrup you mouth!" from The Adventures of Rocky and Bullwinkle and Friends.
The joke on Comic Book Guy's shirt is a reference to the books of Dick and Jane written in programming language, it says "See Spot. See Spot Run. Run, Spot, Run", a popular catchphrase in that book series.
The law proposed by Comic Book Guy about human reproduction is a reference to the mating in the ficctional specie of Vulcans,from the Star Trek series.
In the dog track scene, Mayor Quimby can be seen in the stands, although he earlier fled Springfield thinking MENSA had heard of his corruption.
When Lisa is writing the letter, his typewriter is facing the wall aside to the shelf, but when Homer leaves the room, it's facing the wall opposite to the shelf.