Skinner yelling "Tomorrow is another school day!" parodies the last scene and line from Gone with the Wind: "Tomorrow is another day," with Springfield Elementary standing in for Tara.
When Patty tells Skinner "Good night, sweet principal," she is parodying a line spoken by Horatio after Hamlet dies: "Goodnight, sweet prince."
When Skinner says "Callooh! Callay!" in the bell tower, he is quoting from Lewis Carroll's nonsense poem "Jabberwocky."
While shopping for engagement rings, the opportunistic assistant claims that "a good rule of thumb is two years' salary," a misrepresentation of the De Beers ad that tells prospective grooms to buy—and prospective brides should expect—a ring worth two months' salary.
It's revealed that Selma is two minutes older than Patty.
Homer considers Apu as a husband for Selma. Apu and Selma later slept together after Homer and Marge's second marriage. ("A Milhouse Divided", "Wedding for Disaster")
When Homer is trying to find a boyfriend for Selma, Carl Carlson is incorrectly named "Karl."
When Patty says "Marry me, Patty" after looking at the message on the field, she doesn't open her mouth.
After Bart used herbicide to write his name in the grass in 40-foot letters, Principal Skinner punishes him by making him re-seed the lawn by hand. This, however, wouldn't work, as the herbicide would kill all the seeds; the topsoil would need to be replaced first.
Barney is at home when he rings Homer. Homer then rushes off to tell Marge about the BBQ restaurant, Marge immediately rings Selma at the DMV, and at the DMV is Barney. It would be impossible for Barney to clean himself up and get to the DMV in that short space of time.