The flag in Miss Hoover's classroom has 25 stars and 15 stripes. If she wanted to pay homage to the 1796 American flag, there should have only been 15 stars.
Diphtheria is a respiratory condition which is spread by saliva and causes inflammation of the nose.
The words "cromulent" and "embiggen" were both coined by the writers of this episode. Although completely made up, these words have since taken on a life of their own via the Internet and other media. "Cromulent" has also appeared in the Webster's New Millennium Dictionary of English.
Coincidentally, Donald Sutherland played a character named Homer Simpson in the 1975 film "The Day of the Locust."
This episode establishes that Kearney is older than any elementary school child should be. Not only does he shave, but Principal Skinner names him as the only person who is old enough to remember the 1976 Bicentennial (and, according to Kearney himself, the Watergate Scandal).
"Hollis" and "Hurlbut", the first and last names of the curator, are freshman dormitories at Harvard.
Apu refers to himself as a "semi-legal immigrant," which would later be explored in "Much Apu About Nothing."