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Well, the series is about saving the world, in a way.
The first episode of the anime is pretty heartwarming all the way through, due to the deep idealism inherent to the Demon King's plans being played up to the extreme.
"Maou-sama, this cottage is too big for me to handle alone. May I hire some maids?"
The look on Head Maid's face when Little Sis Maid gives her the present.
After Hero has been in the Demon World for almost a year, war is approaching and Maou begins to have doubts for the first time. She quietly says to the doll she received for the festival that she wants him to cheer her up. Hero walks in the door and does just that, having teleported home to spend the festival with her.
Maou reveals her identity to Lady Knight, who reveals she already knew and has chosen to believe in her and Hero anyway.
At the victory party, Female Knight and Hero share a moment where Female Knight nearly confesses. Archer pulls a Moment Killer, and shoos Female Knight back to the party where everyone is looking for her. However, he then has a truly heart warming moment where he apologizes for isolating Hero due to his overwhelming power, and swears to help create a place where Hero won't be isolated again.
When Demon Queen is possessed by a Demon Lord, Head Maid recites all of the reasons why she followed Demon Queen in the first place, which is why she'll never follow something so lowly as a Demon Lord.
In episode 5, Hero saves a demon girl from getting raped.