In Episode 2, there has just been a notice coming from all the remaining human cities aren't sure they have enough power to survive. Just as it looks like Yamato isn't going to have enough power to launch before getting hit by the giant nuclear bomb, every city on the planet sends energy they cannot spare to Yamato to get her off the ground in time.
Deslar's Pet the Dog moment in episode 8. Shultz and his crew of second-class Gamilas have just died fighting the Yamato, their direct superior Goer is trying to blame them for the failure of the operation (planned by Deslar himself), and Deslar replies by cutting off communications with Goer and ordering that Shultz and his men are promoted two ranks posthumously (incidentally making Shultz of higher rank than Goer) and their families made honorary citizens (of higher social position than pureblooded Gamilas), and puts the blame of the failure on the Yamatobeing just that good.
On Erich Domel's way to receive a promotion from Deslar, a little Garmillan girl is seen running up to his motorcade, a bouquet of flowers in her arms. Two guards chase after her, but Domel calls them off as he kneels down and accepts the girl's gift. It's quite easy to see here that Domel's military accomplishments aren't the only reason why he is beloved by his people.
In episode 17 many of the crew are discussing about Yuki being Human or Iskandarian, with the latter being considered bad. Upon hearing such a discussion, Shima butt in, stating that they had better things to do during a mission and making clear he doesn't care: Yuki is Yuki.
Redof Hyss, Vice President of the Empire, gets one in Episode 23. The Gamillan palace is about to be evacuated because Desler is making a Colony Drop on it and the surrounding city. Hilde Shultz, the daughter of the above, gets trampled down in the surrounding chaos. Hyss, while fleeing, sees this and picks her up. The second highest man of the Gamillan Empire stops and picks up a servant girl and carries her out. Its just a beautiful moment showing that while they are the enemies, not all the higher ups in the empire are evil.
Then in episode 24 he helps convincing Starsha in giving the Cosmo Reverse to Earth as a way to repay the Yamato for preventing the Colony Drop.