This episode becomes more depressing after many bullying-related murders and suicides hit the news, specifically what happened to Phoebe Prince.
An earlier episode, "The Joy of Sect", shows Springfield being outright cruel towards a football team for losing a championship match, even going as far as to attack the players. This also leads to Fridge Horror where it's possible that, had Bart not attempted suicide, the entire town might've murdered him for the same reason as the football players.
A later episode, Money BART, has Bart losing another game (because he tried to steal bases) and everybody (comparatively) being ok with that and Lisa giving Bart kudos. The fact that the focus of this latter episode was Lisa learning An Aesop of "win or lose, the important thing is to have fun", some critics were quick to label it as yet another example of Lisa's Mary Sue/Creator's PetDouble Standard moulding the plot.
Despite this episode being hated for showing Springfield as cruel enough to drive a ten-year-old boy to suicide, the scene of Marge calling the town out for what they've done and arranging a new game to pick up Bart's shattered self-esteem is a bright spot in an otherwise pitch-black episode.
Also, there is LaBoot trying (and failing) to save Bart, even though he was very evil to the boy earlier in the episode.
Never Live It Down: While they did apologize to Bart, many viewers see this as "too little, too late" and would never see any citizen of Springfield (excluding Lisa, Maggie and Marge) the same light ever again. Some fans even wish that the Simpsons would move out of that evil town for the sake of their safety, given Bart was at risk of being murdered until Marge snapped at the townsfolk.
Nightmare Fuel: Just the fact that such a seemingly cheerful, quirky town like Springfield would do something so heinous as what they did to Bart alone counts as this, especially to a number of long-time Simpsons fans who saw the episode for the first time.
Some Anvils Need to Be Dropped: As much as some people hate this episode, it does show that publicly shaming someone over something minor can have an adverse effect on their psychological being.