Principal Shepherd calls out Zack Morris for stopping time to talk to the camera, a frequent device the character used on Saved By the Bell.
While undressing himself, Peter attempts to have an intellectual conversation with Brian, referencing the Three Little Pigs.
When Peter is a garbage pile, and mentions that he "will assimilate this new smell into the larger Borg of my smells." This is a reference to the alien species "the Borg" first shown in Star Trek: The Next Generation, who assimilate other species into their cyborg collective.
After Meg kisses Mental Mike, he says "Your kiss is definitely not on my list!". This is a reference to the 1980 song "Kiss on My List" by pop duo Hall & Oates.