Matt Groening's name appears first in the list of gay people. In fact, the entire list is made up of crew members who worked on the show, all of whom had to sign waivers in order to have their names on that list.
When the comet flies over the Springfield city zoo you can see penguins flying away from the comet, a parody since they can't fly. It could also be a reference to the novel "The Hitchhiker's Guide to the Galaxy", where dolphins fly off Earth prior to its' destruction.
Homer tries to comfort his family by telling them that the comet will burn up in the atmosphere and whatever's left will be no bigger than a Chihuahua's head. When Bart eventually picks up the little piece that remains of the comet, a Chihuahua is standing next to him; a clear reference to Homer's earlier remark. Implying, he has some knowledge about rocks or asteroids.
Everyone getting angry and wanting to come into Ned’s shelter is a reference to "The Twilight Zone" episode, "The Shelter".
The "Three wise men" constellation is representing the Three Stooges' faces.
For a couple of seconds when Homer tries to get the shelter door shut when everyone gets in, Waldo from "Where's Waldo" appears rather obtrusively on the left half of the screen. In subsequent views of that shot, Waldo is replaced with Mr. Spock of Star Trek.
Skinner curses Pierre Jules César Janssen for having invented helium, even though helium is a naturally-occurring element and would have to be discovered. On top of that, Janssen didn't discover helium by himself (also a goof)
Buttzilla, the other name for the weather balloon prank by Bart, is a play on to the name of the Japanese monster known as Godzilla.
The siren raised by the observatory to warn Springfield about the comet, is the same as the air-raid siren to warn British people about Nazi bombings during the Blitz.