The opening scene with the various circus babies being delivered to their mothers.
Just any scene with Dumbo and his mother.
Timothy's friendship with Dumbo. He becomes a sort of substitute parent, who looks after the little guy when he sees he needs a friend.
How Dumbo always holds Timothy's tail, the same way a child would hold the hand of his/her caretaker. (And which young elephants will often do in real life, usually with their mothers.)
Just the fact that Timothy managed to arrange a visit for Dumbo to see his mother, shows how much he cares for his friends well-being, especially given the abuse that the poor little elephant just went through with the clowns.
The sequence was storyboarded by Bill Peet, who writes that he drew inspiration from having just had his own first child at the time. Awwww.
One of the clowns actually showing sympathy for Dumbo when the others suggest raising the platform of the house, when he says, "Don't hurt the little guy." However, this is immediately squashed when the others suggest that "elephants don't have feelings" and that "they're made of rubber".
Dumbo finally discovering that his handicap-his large ears-give him the unique ability to fly. And the final scene where he loses his supposedly "magic feather" but still flies due to sheer will power, amazing everyone in the process and then punishing everybody who was ever mean to him: the circus ringmaster, the clowns, the other elephants...
The end where they wave goodbye with their trunks.
The entire ending. Dumbo flies down into his mother's arms, covers her face with kisses, and throws his ears around her in a hug. Meanwhile, one of the crows is calling out, "Happy landings, son!"
Though they're initially mocking, the way the Crows rally together to help Dumbo learn how to fly after hearing of his troubles is really sweet.
Just the fact that the crows weren't mocking Dumbo's ears like everyone else has. They were actually mocking Timothy's strange idea of an elephant flying. And judging from their tears after being called out, it's pretty clear that if they knew about Dumbo's struggle to find his self-worth, they wouldn't have had mocked Timothy's idea.
This◊ editorial cartoon done in response to Ringling Brothers announcing their retirement of elephant acts by 2018.
The newspapers at the end have articles on World War II, and one of the images shows "'Dumbombers' for defense". After the outbreak of WWII, Disney began designing military insignia. Dumbo was featured in several.