Warning: Spoilers Off applies to these pages. Proceed at your own risk.
The way Jaune is being viewed by his students is a constant source of hearth-warmth. Insulting him or accusing him of something is enough to make Pyrrha despise you.
Ruby's You Are Better Than You Think You Are speech to Jaune certainly qualifies. For all the schemes and lies Jaune has been producing, hearing that his efforts at helping his students out were not in vain is well-deserved and very touching.
Velvet desperately attempting to save Pyrrha after the latter has been nearly drowned. It shows that even if Velvet doesn't care much for her new team, she will still not let her teammates die under any circumstances. It also doubles as an unusually heartwarming subvertion of a Sadistic Choice; the decision between chasing down a criminal and saving her partner is by no means hard for the huntress.
The relationship between Jaune and Neo is very heartwarming, even despite all the beatings she is handing out. Neo is, at the end of a day, the only person Jaune can trust completely, and the one to pick him up in his most miserable moments. Chapter 41 probably illustrates it the best.
At one point, Neo even offers Jaune some of her ice cream when he's depressed.
Jaune: "I don't want to be a hero. I don't care about reputation. I don't care about what people think of me, I don't care about being a hero. The reason I'm doing this is to protect the people I care about; my students, my colleagues-everyone at Beacon. There is no other reason!"
Blake, who was watching the fight incognito, is incredibly touched by Jaune's remarks, and grows to admire him more.
The heroes managing to prevent Penny from getting murdered. Having her alive and mostly in one piece is nice enough, but it also works as a reminder of how Jaune's actions really did make things better.
When Jaune finally confesses to the Beacon staff, they all more or less forgive him, acknowledging that despite his lies, he still did a lot more good than bad. Even though Glynda is understandably enraged, she still cares for Jaune despite everything.
Before Cinder manages to kill Pyrrha as she did in canon, Velvet jumps to save her partner, despite their history and the danger she is putting herself in. Bonus points for Velvet using a copy of Crocea Mors.
Professor Arc II
Weiss admits that given the choice between her dream of running the SDC and being on Team RWBY, the latter wins every time.
Oobleck mentions that he and Roman are on good terms now that they've had a chance to reconcile.
When ambushed by Salem's forces, Ozpin swears on his honor as a knight and king that he'll do his best to get Oscar out alive despite them both knowing Ozpin doesn't actually lose anything by dying.