Angst? What Angst?: Later episodes that focus on Bart having to repeat the fourth grade wouldn't have him react as desperate as he did here.
Family-Unfriendly Aesop: The episode ends with the ultimate moral that failure is an inherent part of life, and that we can all fail sometimes, even when we try our very hardest (sure, by the end of the episode Bart has improved—but only marginally, and clearly not enough to deserve the pride and respect of his family). Some fans have actually praised the episode for not being afraid to broach this topic, and for unapologetically breaking it with the standard happy ending where perseverance and dedication always results in success.
Growing the Beard: Widely considered to be the episode in which the show really gained its own voice, proving that it was more than capable of being both funny and emotional.
Harsher in Hindsight: Despite Bart earning his happy ending and actually passing his history test, later episodes would still have him in the fourth grade, making this whole episode a complete waste.
Bart's Imagine Spot of him repeating the 4th grade as an adult decipts Edna as an elderly teacher. Edna didn't live to old age as she was killed off offscreen due to Marcia Wallace's death in 2013.
Memetic Mutation: The infamous scene of Bart crying over his F shows up quite a bit on Tumblr.