Hibari's affection for Densuke, especially when you learn why she named him Densuke. It's in memory of her stillborn baby brother.
Episode 18 has Takashi's lack of respect from his father despite everything he's done, leading him to arrive at Jun's apartment in tears.
Episode 19 has the Sibyl Team's passionate declaration of love, even if it means they're martyrs for it, which even stuns Hibari.
Episode 20, from start to finish, details Tsubume suffering an emotional breakdown when she sees how a loving family behaves.Hilary Haag captures it perfectly.
Tsubame Ohtorii: "You're nosey, Hibari... It's not fair! Why should you have everything? Why is it always about you? Hibari has a father who loves her! Hibari has a mother who loves her! Everyone is doting all over her! Hibari has a place to go home to! Why do I have nowhere to go? No one doting over me? It's just not fair! All I want is..! ...Is..." * sobbing*
Episode 25, when the girls are spending their last day on Earth before leaving, and are contemplating all the loved ones they'll have to leave behind.
Episode 26, when the Pata-pis all develop souls and free wills and decide to go with Crane in the girls' place, and all the girls, even Tsubame, are crying and begging them to come back.