In Chapter 39, even though the situation is bad, Quiet Presence calls Spike a hero:
The Lord of the castle is leading the Bearers down a secret passage filled with traps. There's every chance that if I saw this in a story, I might start shouting at the page in a completely futile effort to keep the heroines and hero from going in there."
Chapter 53. Discord claims all the hybrids as his, claiming that he's tied to the land, to children. Part of his fury against Gentle Arrival is clearly fury about what he's done to her, and he offers not only recharge the chaos pearls if needed (so long as he is asked first). He also offers, of his own free will, to train her in her powers.
In Chapter 55, Discord's surprisingly gentle and paternal interactions with her. He also offers sincere comfort to Twilight, who is currently reeling emotionally from The Reveal that she is — or, at least, Celestial believes that she is — Star Swirl's magically-induced reincarnation. Discord comforts her by pointing out that even if this may be the case, she is not Star Swirl. She is her own pony, and has the chance to live her own life, and he encourages her to do just that.
Also in chapter 55, Discord's genuine empathy for Triptych, talking about how she spent her entire life imprisoned utterly, with her only hope for escape being the ability to hope somebody would change. The last thing he says, the last line of the chapter, makes it clear that Discord really has found some understanding of empathy:
Discord: "No one should ever be trapped in stone."
Chapter 56. The whole thing, really. Everyone is healing. It's taking time, but they are recovering, thanks to each other. Even Twilight, after having her faith in Celestia shattered, is willing to extend an olive branch. She's not ready to forgive, to talk yet, but she's willing to give it a go eventually.
Applejack's decision to ask Snowflake out on a date is extra heartwarming with the hindsight that, 1: Drunk Little Ponies revealed she's been interested in him for a long time, 2: Snowflake has basically resigned himself to a life of being alone for his looks, as seen in Scootalift, and 3: this shows how Applejack has finally managed to shake off her own unconscious tribalism, allowing herself to ask out the pegasus she wants to date instead of trying to find an earth pony because she's supposed to be with one.
Applejack managed to get a special dispensation from Princess Luna to use the confiscated snitcher on Apple Bloom... and it confirmed that her mark magic is finally on the rise.
In Other Stories:
Twilight's friends gathering around her in a ponypile in 100% Move = 50% Fire after she confesses to her fears of driving them away, with each explaining why they will continue to love her and forgive any mistakes she makes along the way no matter what happens, because they know she's trying.
Cranky talking Pinkie out of her depression following her inability to make a soufflé, slowly getting to the core of why she hasn't been able to pull it off without hurting her or making things worse. He works out that to some degree, she's been subconsciously sabotaging herself because if she does make the dish, it'll be the first step in having to eventually leave the Cakes behind — something she's not ready to do.
One of the themes in Princesses Can't Cook is how taste and smell can be the best way to awaken memory. Celestia and Luna initially ignore it in favor of starting into the actual cooking process — but in the end, it's a lesson they learn. The hard way.
It's a darker example than most, but Celestia and Luna's worst-case scenario talk in Chapter 8 of A Mark Of Appeal is a quiet demonstration of how much they truly love each other. Enough, if things went as wrong as they possibly could, to give each sister responsibility for helping the other commit suicide.
In Stupid Direction-Face, a minor example is The Reveal as to why Garble is so intent on growing bigger: he wants to find a way to keep his friends after reaching adulthood, instead of giving in to instinct and driving them away to protect his hoard.
In the final chapter, he then succeeds in using The Power of Friendship to retain his mind after a greed-fuelled growth spurt. As with Spike, this reverses the surge and leaves him at his normal size — which makes him more than a little vulnerable when the hoard's true owner finally shows up. And his father is not happy.
Despite himself, Snowflake actually seems to be turning into a more or less successful mentor-figure to Scootaloo in Scootalift, giving her an adult who'll actually listen to her and who actually could be a moderating influence — in contrast to Rainbow, who does like her but... doesn't exactly keep anything under control.
One chapter also involves a display of how the Crusaders are more than just the town's hated idiot anarchists; to each other, they're true and loyal friends, to the point that Snowflake realises that Scootaloo has a support network he never could have dreamed of having when he was a colt.
Chapter 25 of Triptych. The Nightmare attempts to subsume Twilight... and the memories of her friends are what save her from it.
Despite mostly being a comedy story, Sick Little Ponies (And One Dragon) actually has some fairly heartwarming moments to it.
There's the family bonding between the Apple youngsters at the end of Applejack's chapter as they sit, look over and talk about the photos of their deceased parents.
In Spike's chapter, not only do we have the police of Ponyville absolutely refusing to do anything to hurt Spike despite the Flower Trio's fear-mongering efforts, we then have Mr. Rich calmly stepping forward to get the sick little dragon what he wants and taking him home safely, ending with Miranda Rights, the Ponyville chief of police, assuring Twilight that Spike did nothing wrong and, even with the Flower Trio being idiots, nopony is going to blame Spike for anything. This chapter is hugely improved if you read Unnoticed, a Tearjerker-rich story about how Spike is initially seen by the ponies of Ponyville, beforehand — the change in attitude is marvelous.
Ultimately, The Bounce Test is about Flash Sentry being made to reframe his entire life, going from Walking Disaster Area to a talent-powered Destructive Savior who sets off small accidents in order to defuse huge ones. Iron's attempts to talk the pegasus into truly seeing himself for what it is are oddly endearing, especially when it becomes clear that Flash's reputation has left him with no friends anywhere along his long transfer-filled road to the Empire — and the next-to-last scene, as every Guard (plus Cadance) approaches Flash to thank him for saving their lives, comes close to Tearjerker territory. Until that moment, practically no one had ever thanked Flash for his sacrifices, or even realized that sacrifices (of reputation and self-esteem) were taking place.
On the whole, the relationship between Rarity and Twilight can qualify for this. Rarity serves as a Cool Big Sis for all of the Bearers on her good days, but it's Twilight who needs that connection the most. Other than Spike, Rarity is the most likely to keep Twilight centered and focused, which can sometimes include reminding her of just how far she's come since getting off the air carriage. But there's a price to pay for that, as Rarity is also the one who often has to tell Twilight things she doesn't want to hear, and it leads to ebbs and flows in their friendship.
The final scene for The Remainders Of The Day has Twilight trying to repair her relationship with the mayor by gifting her with a copy of the encyclopedia volume which brought Marigold to her mark. It's a sign of how much progress Twilight's made since arriving in Ponyville, and while the mayor seems to initially openly dismiss the offering, Twilight gets to hear the mayor's forehoof gently rubbing against the book's spine.
"Volume Seven," the mayor whispered. "My Volume Seven."
Twilight looked back, and saw the shine in Marigold's eyes.
In a way, A Confederacy Of Dunce Caps isn't just about Diamond losing her status as Karma Houdini, it's also about her learning to trust. Ultimately, she has to open up to Snips and Snails, telling them the truth about why she's been going so far to make them study: so she can copy off their papers and pass herself. It leaves her facing the ground, blaming the local pegasi for why the dirt is getting so wet, listening to the boys trot away while they talk to Silver about it — and then they come back to her, unsure of how they feel about having been used, but willing to postpone any reaction until after they help her study for finals.
On a smaller level, Diamond's relationship with her first pet: the jeweled scarab Cameo. She truly does everything she can to take care of the insect. Managers have to look after their employees, and since Cameo's job is to make Diamond happy...