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.
Jaune, reminiscing during the fight on his father's Semblance, which lets Nicholas Arc tell when it will rain, notes that his father insisted that he would never want a more combat-oriented power, since the Semblance he has far better allows him to help his wife.
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.
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.
By the time Oscar and Ozpin reach Beacon, Cardin as developed to an outright Nice Guy who warns Oscar about being racist, citing that racists are "fuckwits and nobody likes a fuckwit".
When meeting Jinn, Ozpin apologizes for leaving her locked away with nothing to do, saying that he hadn't intended to be cruel when he did so. Jinn easily agrees as she's always known his reasons and knows his apology is sincere.
After a pep talk from Qrow, Winter finds a way to let Weiss reunite with the rest of Team RWBY.
While on a call with Ghira, Blake takes the time to tell him she loves him and apologize for joining the White Fang.
In the following chapter, Jaune makes very clear he will run over anyone who gets between him and getting Neo medical treatment.
All of chapter 57, really. After the complete victory against the Grimm in Atlas, all of Vale's Hunters are praised as heroes, and they return to a massive celebration in their honor. Everyone is happy and proud of their achievement, and even the attack on Shade can't bring their mood down.
Ozpin is saddened by the fall of Shade, since he was the one who founded the academy. However, Oscar breaks him out of the mood by reminding him that Shade falling wasn't his fault, and that he already did all he could by founding Shade Academy in the first place. In turn Ozpin commends Oscar for being selfless and brave enough to sacrifice some of his limited time allowing Ozpin to take over his body so they could fight.
Ozpin: "You know, when the God of Light cursed me with this, he told me I would reincarnate in the bodies of those most like myself. I was a knight before I was a king. A warrior. A hero. And I think I see now why you were chosen."