The Doctor notices the TARDIS has a lot more bedrooms and kitchens than she ever had before and starts to wonder why. He eventually realizes that the TARDIS reformatted herself to encourage The Doctor to keep the Mane 6 around.
Game of Stones
The Doctor immediately coming to Sweetie's aid after she breaks Rarity's clock.
Applejack immediately declaring they have to help find The Lost
We find out that Leonard used Twilight as the model for the pony equivalent of the Mona Lisa.
The bittersweet romance between Leonard and Twilight, once Twilight reins in her fangirling over being in the presence of a scientific and cultural icon. They only get one night together, but it's one night between two ponies who have extraordinary respect and admiration for each other and as mentioned above, Twilight continues to be Leonard's muse long after she and the Doctor have to leave.
A sort of Meta-Heartwarming moment is that the Anasi is actually one of the spiders from Planet of the Spiders rather than one of the Racnoss. Most fanfic writers have a tendency to focus entirely on the New Series and draw little from the Classic Series, so it's nice to see that that isn't the case here.
The Doctor leaving Zecora a letter of apology.
Doctor: It’s not everyday one sends a bouquet of poisonous ferns to try and make amends, but I suppose there is a first time for everything. I do not know how long you were standing there, and I’m sorry if what you heard that day scared you, but while I cannot honestly deny ‘all’ of Anasi’s words, I promise that what she had to say was not the whole truth. If you ever want to talk about what happened… or if you ever need help: Press the button. If not, then I can promise that you will never see me again. I cannot express in words how truly… deeply… sorry I am that events came to pass as they did. I never wanted to frighten you. Until next we meet, should you deem it to be so, The Doctor.
Somewhat of a Tear Jerker, though, as it's implied that Zecora is still too terrified of The Doctor to take him up on his offer.
The Reveal that Fluttershy's bravery led to Zebrica turning into a beautiful, fertile land.
Pretty much anything involving the next generation of Cutie Mark Crusaders. Dawn, Cream, and Daring, whom are all but outright stated to be Twilight, Pinkie, and Rainbow's daughters. Sort of Fridge Heartwarming is that their families are still friends after all these years, especially since it is established they've met the old crusaders.