Homer's grease heist scheme might have been inspired by the Fight Club novel, although the episode aired over a year before the movie based on the novel was released, giving it more mainstream fame.
When Marge is dancing, her eyes are briefly so low down that they cover almost the entirety of her nose.
Despite being the first day of school, a calendar in the back of Ms. Hoover's classroom says March. Ms. Hoover is lazy and does not care much for being a teacher. Her neglecting to change the calendar is not out of character. However, at the grease collecting plant, the calendar shown in the background also says March.
There appear to be four of the same faced squeaky voiced teens at Krusty Burger.
When Alex is complaining to Lisa about the students' childishness, Sherri and Terri are bright yellow instead of pale yellow.
Jimbo, Kearney, and Dolph are missing at the school. Given their characters, it's plausible that they were either suspended or skipping school, or that they just were not interested in the dance or the particular events of the episode.
In some FXX reruns, from the part when Lisa says "Enjoy the dance" to Willie shrieking seeing Bart and Homer, the talking and sound effects are out of sync.