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.
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.