Izumo is the only one to not care about the fact that Rin's the son of Satan. Rin is touched. Izumo is not.
"Shiro, you weren't raising a weapon. You were raising a son."
ALL Chapter 11 and 12. Until Amaimon appears.
On a mission in an amusement park, Shiemi wishes that she could come again when they're not on a mission. Rin tells her that next time he'll go with her and Shiemi agrees.
When Rin is suffering from crippling self-doubt expressing itself in rage in Chapter 26, he receives a Cooldown Hug from Shiemi, who hugs him despite Rin being on fire at the moment, proving her trust for him and renewing his hope.
Fujimoto's contingency should he die and Blackie find out - the wine they became friends over years ago.
Episode 19 is this for everyone.
In Chapter 32, while Shiemi tries to save her, Izumo yells that she hates Shiemi. Shiemi's reply is that she still likes Izumo and thinks of her as a friend even if she hates her.
Chapter 44: In the previous chapter, Rin revealed his half-demon nature to Godaiin and later gave him the eye drops to get rid of his ability to see demons. In this chapter, Godaiin (who had been rather freaked out by Rin's revelation) reveals that he's held onto the drops, but hasn't used them. He explains that he's scared, but he has a dream, and friends and family. Rin is annoyed since he worked hard on getting the eye drops, but the two converse like friends anyway.
Chapter 47, despite probably wanting to dance with Shiemi alone, Rin decides to respect her wish to cheer up Yukio by having all three of them dance together. His thoughtfulness touches Shiemi greatly, although it just plain puzzled Yukio.