Maou, despite being the DEMON LORD whose name is Satan, is a really nice guy.
Aside from their mutual snark exchanges, he actually treats Emi with relative respect, despite the fact she pretty much destroyed his empire.
Alciel is extremely loyal to Maou, acting like his parent/spouse at times and even foregoing his dignity if it benefits Maou. Maou is also very kind to Alciel; after Alciel is shot in the chest, Maou's first thought is to get him to a doctor and carries the larger Alciel on his back, even after getting shot himself.
Even in regards to civilians that he plans to rule over, he shows enough concern for their well-being to use his powers to save them after the mall collapse, deciding that rescue workers would take too long to respond.
Emi, despite being a bit petty and being trained to be a Blood Knight hero, has a heart of gold as seen in her interactions with Chiho.
She even seems to actually care for Maou and Alciel's well being; she asks if Alciel is okay after the mall cave-in, and she seems very distressed when Maou is shot through the chest. Plus, she doesn't kill them when she has the opportunity to. She is actively going against her training, experiences, "destiny" and longstanding core biases against them and listening to her better judgment as a human being, realizing that those two are no longer the monsters they were. Her constant snark, irritability and hotheadedness seem to stem from her constant efforts to avert a lifetime of experiences that are now contradicted by her present environment. If words concerning her supposed "destiny" are more than rhetoric and hold weight, then she's fighting against fate itself.
In the first light novel, when Maou becomes extremely happy when he gets his first raise and Alciel is so moved by this that he cries.
What she says during the previously mentioned walk. Why she stuck around and still loves him even after learning the truth and what Emi told her about his past. That falling in love is her decision and falling out of it will be hers as well. Stating how she'll understand if he doesn't see her that way, that he doesn't need to and that she's not dependent on it for her to love him. All this and more during their walk. Her implicit trust of him when she's in danger is conveyed often in her actions, gestures and in her words during the show.
She's also not afraid to get angry with him when he pisses her off (unintentionally). She gets pretty pissed and scolds him harshly when he states he has just enough magic that, if she wants, he can make her forget all about him and recent supernatural events.
Lucifer of all people gets one in Episode 12 when he betrays Olba, prompting Olba to ask him what happened to wanting to return in Heaven. Lucifer's reply? "Heaven is a place on Earth, in an apartment the size of six tatami mats." He said it because he enjoys the NEET lifestyle, but it is still incredibly heartwarming to hear especially since he was the antagonist not seven episodes ago.
Suzuno finally completing her Heel–Face Turn, deciding to stand against Sariel for the sake of her friends. Also her apology to Chiho later.
Episode 13: It's a heartwarming end to the anime.
Emi willingly helps the demons out of a scam.
In a call back to the first episode, Maou is caught in the rain without an umbrella. He then meets Emi at the same crosswalk they first met on Earth. Emi gives Maou a new umbrella to make up for destroying the one Maou gave to her. After he thanks her, she simply smiles and spins her umbrella.
Alas Ramus' interactions with Maou and Emi are adorable. Things such as going to an amusement park and spending the night together almost make you forget that they're a Living MacGuffin, a demon lord and the hero respectively.
In Volume 4, as the action ramps up in the end, Maou's gang is very suspicious of Amane Ooguro. At one point, Amane appears out of nowhere in a fog in front of Suzuno and Chiho. Suzuno throws herself protectively in front of Chiho to protect her friend. As Amane Ooguro is an aspect of Binah and is a spirit of the Earth itself, her power is off the scale. If Amane was hostile, it would be like one fly trying to protect another. It is still heartwarming to read of Suzuno being so protective of Chiho even in this impossible situation.
The Confessional scene between Maou and Suzuno, or rather, Crestia in her Church role, in Volume 9, where she hears the true reason of the invasion: that Maou is trying to save his people from eventual starvation, and forgives Maou for his invasion of Enta Isla.
The surprise birthday party for Emi in Volume 11, especially given that the rescue mission staged in Volume 9 and 10 is partly due to her not coming back for her party as promised.
As funny as it is heartwarming, Laila's absolute mess of an apartment in Volume 13 finally gives something that allows Emi to see her as a person, and allows the two to slowly reconcile.
