Signature Scene: Homer losing his temper with some kids trying to get a peek at his hooks, and breaking them through a window.
Strawman Has a Point: One guy in a diner tells Homer that the military basically duped him and cost him his hands. While one could hardly blame him for being upset, since the Nazis and Japanese might have done more damage, had he not been in the war, there is no debating that he still would have had his limbs intact (to say nothing of the fact that the conflict with the Japanese was pretty much resolved with nukes and Hitler committed suicide, so U.S. troops might not have been needed).
Tear Jerker: The scene with Homer returning home, where his own mother gasps in horror upon seeing his metal hooks. And Homer flashes a pained expression across his face...
A real life example: The man who played Homer went bankrupt after this movie and ended up having to sell his Oscars.
Towards the end, as Fred finds himself in the bombers' graveyard, row upon row of rusting hulks no longer needed with the war over, symbolizing his own worthlessness as a war hero with nowhere else to go. When he crawls into one wreck to relive yet another flashback, you're crying for him. Subverted when he's discovered by a guy overseeing that graveyard who's starting a project to break the hulks down into metal housing for the families of returning war vets. Fred finds out they're hiring.
Values Dissonance: To modern viewers it can seem pretty odd how little attention Al's obvious alcoholism gets.