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The reason why Vinyl was willing to eat Octavia's horrible apple/mushroom pie:
Octavia: And if it was really that bad, why did you nearly eat the whole thing all by yourself?! Vinyl: Because you made it for me! [pause] Vinyl: [Sighs.] Spitfire, you asked that you wanted to know what itís like living together with Octavia? For serious? Spitfire: Yeah... Vinyl: All joking aside ... I get to wake up every day, living with the pony who makes me the happiest. I get to laugh together with her, joke with her, and just be there with her. Every second Iím with her makes me feel like Iím in front of a cheering crowd after the best set Iíve ever done. Iím ... [Chuckles.] Iím just grateful she somehow manages to put up with me every day without punching me in the face ... I really couldnít be happier than I am, right now.
Princess Luna listening to and visiting Blueblood's radio show, not because it's any good, but because he's her nephew. And she too knows the pain of having everypony hate you.
Season 1 Episode 2 is chock full of these:
When Spitfire tells Octavia why Vinyl is her best friend:
Spitfire: Well, eventually I had to leave for Flight School. We were both still pretty young at the time. Neither one of us had our Cutie Marks. When I told Vinyl I was moving, she didn't say anything. She acted like it didn't bother her at all. Tried to play it cool, I guess. So I ended up going to Cloudsdale to learn to fly. After I was there for a couple months, I got a letter from my parents saying Vinyl was in the hospital. I immediately freaked out and flew home.
Octavia: Why was she in the hospital?
Spitfire: That's exactly what I wanted to know. When I got there, I found out she'd broken her leg. I went right to her room and asked her what had happened. Apparently, she'd fallen out of a tree. She had climbed it, built some little "wings" for her hooves out of cardboard, and jumped out of it. She was trying to fly.
Spitfire: So I said, "Vinyl, that is without a doubt the stupidest thing I have ever heard. Why would you do something like that?" She said, "I wanted to go to Flight School. You have to fly to go to Flight School." As if it was just common sense or something. When I asked her why she wanted to go there, she was quiet for a minute. That was a first, by the way; seeing her quiet about anything. And she just looked up and said, "I wanted to see you again."
Octavia received a ton of appreciative fan letters after the episode. They still adorn the studio walls.
Vinyl framed the picture she took of herself, Octavia, and Spitfire. She keeps it on her desk so that she can look at it every day.
Season 2, Episode 3 is very heartwarming, especially Princess Luna's You Are Not Alone speech to her nephew Blueblood.
Almost all of Season 2, Episode 4. Octavia gathers all of Vinyl's friends—and even Celestia and Luna—to bring her out of her Heroic BSOD. And then there's the end of the chapter, which shows Blueblood (who was about to start yet another Evil Plan) having a Heel Realization, setting up his Heel-Face Turn in the following chapter.
Also, Trixie willing to stand up for Blueblood and call out everyone else's hypocrisy.
Season 2, Episode 5 has one point in the interview, more specifically, where Vinyl talks about how she really wanted a co-host because she was lonely. While Octavia's reaction stirs up some fluff, Blueblood's is stronger. He actually realizes that Vinyl had a point when she said that they were Not So Different from each other. He connects with her, and when he sympathizes with her point, Vinyl, who's been delighted to humiliate him, is happy to see that he's willing to make peace. There are a few afterwards, but that point is what kicks them all off.