A very minor one in Chapter 1. Littlepip reads the override code which will open Stable 2's door, left by Sweetie Belle which is "CMC3BFF" - clearly short for "Cutie Mark Crusaders Three Best Friends Forever".
The end of chapter 17 and opening of chapter 18. After lusting after Velvet Remedy for so long, with little to show for it, LittlePip finds that Homage, the Tenpony Tower unicorn is interested in her. The date they go on is very awww-inducing.
Chapter 22 Littlepip promising an adventure with just her and Calamity after the latter starts feeling left out.
The opening of Chapters 25 and 27 follow Littlepip's thoughts on her companions in respect of friendship and family. Particularly effective in the former as this line of thought leads to her feeling lonely and weak without her friends only to receive a welcomed visit from Pyrelight.
Chapter 28, when Steel Hooves goes on the announcement in Stable 2, declaring to all the true oath of a Steel Ranger.
After Canterlot. When Littlepip is tired, worn out, sick, and at her weakest, the Black Book tries to prey on her, tempt her into using it. Convince her it is the only way for her to survive, to fight. And she nearly gives in, until, the spirits of the Mane 6 step in to help aid her. Countering all the Black Books taunts at Li'lpip. Helping her see her own virtues, giving her the strength to keep fighting. And at the end, showing her how wrong she was about herself. Helping her see just what her soul truly looked like. Not simply a battered, bleeding, dying raider. But a pony willing to sacrifice herself, simply to warn total strangers of a threat. Give them time to save themselves.
That entire chapter was pretty heartwarming. It includes a Thank-You party for Ditzy Doo for saving them from the Enclave.
After killing the Goddess, Littlepip sees that one alicorn has turned purple, with Twilight's cutie mark. Littlepip manages to take the message that Pinkie Pie left before the megaspells hit and play it for her, so that if Twilight is even still alive, she'll know that Pinkie acknowledged she had a problem and really wanted her there with her. Hopefully it got through...
"For the longest time, I had thought of myself as Red Eye’s reflection (granting one of Pinkie Pie’s particularly warped funhouse mirrors). But I was comparing myself to the wrong pony. I wasn’t Red Eye. I was Applesnack."
One moment in the logs of that unicorn scholar that lives in Zebratown. Pinkie Pie and some members of the Ministry of Morale come to Zebratown and at one point hide outside the house of one family. You think they're going to get jumped and arrested...then it turns out that its the birthday of the family's little daughter and the Ministry of Morale throws her a party.
“I’m here. And I’m not leaving you.”
The Afterword, which is just a much as a Tear Jerker too. We discover that Fluttershy was able to recover from the effects of killing joke. But we also see how much it still torments her. We also see happy endings for Ditzy Doo and other characters as well as an optimistic ending.