Pretty much all of Haruto's interactions with Shoko, and his attempts to confess to her.
Haruto's friend requests going through the roof when he wins the battle, and the joyous celebrations of his classmates. Pay attention to the audio and you'll hear some kids boasting about how they're friends with him.
Haruto and Shoko's reunion in episode two.
In episode three, Haruto posts a comment on the website everyone's trying to contact him throughs saying that he's all right. There's an instantaneous influx of people praising him. We see a pair of mothers on earth expressing joy at how he's alive, and an entire soccer stadium cheering about it, with the star team asking Haruto to come by and watch them play some time.
In episode five, the Sakimori students produce a music video to boost the morale of Jiis oran refugees. And it seems to work.
In 'Saki, Come Back', after Saki has written some self-aggrandizing stuff about herself under Haruto's name, using an internet code which required a retinal scan. Regardless, Shoko sees through this, because she knows Haruto well enough to know he'd never praise one person above everybody else so much.
In episode 8, we have L-Elf's first encounter with Princess Liselotte. She saved his life when he was trying to escape from a Dorssian prison by giving him half of hers, which to symbolize she disarms him and cuts off a piece of her hair.
Aina's spirit appearing to Kyuma in episode nine in order to accept his feelings but "dumping him" by telling him not to follow her (get himself killed), helping him have defend the module from a Wave Motion Gun.
In episode 10 we have two notable moments:
Haruto promises Shoko that he will rescue her father because he doesn't like seeing his most important person cry.
Later on during Shoko's election speech, Shoko states that when New Jior arrives at the moon, she will confess her love to the person who thinks of her as his most important person.
Raizo "Thunder" Yamada winds up naming his Valvrave after his dead friend Nobu, and calls it Nobu Lightning.
Haruto proposing to Saki in episode 11.
Saki and Akira, two very different outsiders, helping and warming up to each other in episode 15.
L-Elf dropping the entire operation to go save Lieselotte, despite it putting the entire thing at risk. "Allow me to abduct you" indeed.
A bit of background in this one is that L-Elf tried to run away with Liselotte in the past, but as Liselotte pointed out, there would be no point in running away if they have nowhere to go to. When he comes to get her, he declares that it will be different this time, as he now has a country they could go to.
Saki's rescue of Haruto and L-Elf in episode 22, complete with her crying Tears of Joy.
L-Elf: From beginning to end, we were a terrible team
Haruto: Well, we're polar opposites.
Cain giving up a chance that he might've been able to use to escape his exploding Valvrave to reunite Prue with his sister Pino using the last of his power before dying.
The final scenes of the series, with Shoko greeting the alien infiltrators peacefully, and the cockpit of Valvrave I, full of either Haruto or Shoko's memories (suggesting that they found a way to pilot and fuel the thing without eating the pilots), and the new registration question for the Valverave: "Do you believe in human beings?"
Also, Satomi and Takahi getting married in the aftermath.
And before this, L-Elf in a burst of tears of emotion finally telling Haruto that he was his friend. Whenever he tries to remind the amnesic Haruto of the promise they made together, Haruto gently jabs his face with a smile which implied that he remembered everything.