Chapter 1: Just much Mutsumi is hated in her class. We were never given any reason for their hatred, they just hate her. With some of them even wanting her to kill herself. It is not helped that they bullied her to release stress from exams.
The reason of hatred is implied to be that she refers to herself in third person, which makes this even more of a tearjerker because it's such a dumb reason to hate someone. The resolution's also a bit sad if you see it as a case of victim blaming, wherein Mutsumi's the one at fault who needs to change.
Chapter 11: We finally learn why Yukine, was being such a jackass. He died at a young age, and was jealous of the people still alive. Feeling they had family, a past, friends and a future. When he had nothing.
Chapter 14: Just Suzuha. He admits that due to the large amount of Shiki that Vaisravana has, he's not really called anymore. He stills keeping a dying tree alive as it was a memory of a living girl, that he loved but she has long since forgotten him. It is really hammered home when Kuguha just tells Suzuha, he is completely alone. No human will remember him, and even his goddess has forgotten him. It was so effective Suzuha crossed the Despair Event Horizon and let Nora kill him.
Just how wrong he was. Not only was Yukine waiting for him, but Bishamon realized who exactly was gone very quickly, and remembers details about him like how she found him and how he was mentored by Kuzuha along with Aiha... how all shinki grieve about him and it's clear that in truth, there were a lot of people who cared and never forgot about him, even if none of them were mortal.
Chapter 19: As Yato slays the massive ayakashi formed from Bishamon's corrupted shinki, they cry for their master in their last moments, and Bishamon tearfully begs Yato not to kill them.
Chapter 23: The flashback showing Kazuma's life in Bishamon's first clan of Shinki. When Bisha falls ill, the shinki begin throwing accusations at each other. As a result Touma, the shinki Kazuma was closest to, is falsely accused of being the culprit after standing up to the then-Lead Shinki (indirectly implied to be the culprit herself). The other shinki then threw her into a pit of gloom as Kazuma watched, powerless to save her.
Chapter 42: Despite being a lovey-dovey god-and-shinki pair that acts like a married couple, and Daikoku's love of children, Kofuku and Daikoku don't try to have children (by means of adopting the spirit of a deceased child), which baffles Hiyori. However, Kofuku reveals that they did try to raise a child once, but the fact that little Daigo didn't grow but was at the age where he asked a lot of questions began to take a toll on them. Soon Daikoku ended up stinging his master so much because he lied to Daigo by omission, unable to bring himself to break it to his son that he can't grow up because he's dead. Because of how bad it got, Kofuku had no choice but to release Daigo. They erect a headstone in their backyward in his memory.
Chapter 43: What starts off as another filler episode turns tragic when it is revealed that the old woman's deceased mother, whom she sought to return her bracelet to, is none other than Mayu. The old woman suffers the curse of an ayakashi because of her Survivors Guilt, constantly dreaming about her mother's death during the war. When the affair is sorted out, and the old woman able to return the bracelet to an unwitting Mayu, Hiyori quickly learns that she cannot reveal the truth to Mayu, and by extension Yukine because it delves into a god's most guarded secret: they inherited the lost memories of their shinki's past, and to reveal that knowledge is incredibly taboo.