Twilight's words of comfort after Derpy's breakdown in the library:
Twilight: Derpy. You are not a failure or a featherbrain. I can tell deep down that you are a very kind and intelligent pony. Trust me, Derpy. Most ponies out there don’t look at you for who you are. They see what they feel like seeing and then go on with the rest of their lives, oblivious to what hurt they may be causing. You need to look past that, because the ponies who don’t take the time to care, don’t deserve the satisfaction of making your life miserable.
Derpy: How can you possibly...
Twilight: ...Know that? I know that because up until two years ago that was an exact description of me as well. Before I moved to Ponyville, I had one friend – Spike – and I barely treated him as a friend, more like just a helper. I didn’t understand the effects that friendships can have on ponies or how much they can infinitely change your life for the better. I think that this may be your first hurdle to a happy life, when you realize that your life is what you make of it, not what others tell you it is. You need to start with finding a true friend, a friend who will share in your joys, sorrows, pains, and help lift you through the difficult times when they come.
Derpy: Twilight, you’ve seen what a mess I make of everything. You’ve seen the looks ponies give me. Where am I supposed to find a true friend when I can’t even find a pony that will put up with me for more than a day?
Twilight: Well… ever since I came to Ponyville, I’ve made many friends, and I’m sure you know that Applejack, Fluttershy, Rainbow Dash, Rarity, and Pinkie Pie mean the world to me. I don’t think that there is a limit on the number of truly dear friends I can have, so... I’d be glad to have you as a close friend, too.
When Twilight offers to take Derpy on a tour of Ponyville to prepare for her new job, Derpy is reluctant, as she doesn't want to risk damaging Twilight's reputation by being seen with her.
Twilight: Derpy, listen to me, and don’t ever let yourself forget what I’m about to say. I don’t want you to think, ever, not even for a moment, that I would be embarrassed by you. If I was that concerned about my image that I’d avoid being seen with you, then I wouldn’t be your friend in any sense of the word. I meant every word that I said to you, Derpy. You are my friend. I am not going to throw away something so important because some random judgmental ponies out there think it’s strange that I like you.
Post Haste, the head of the Ponyville postal service, gets one in just about all of his interactions with Derpy:
In Chapter 4, he praises her performance on her first shift in Ponyville and offers her the job that the Cloudsdale office just fired her from (over an accident that wasn't her fault).
In Chapter 5, Derpy tries to pre-emptively apologise for the mistakes she's likely to cause. He makes it clear to her that unlike Crafty Crate, he will support his employees through anything, and that she's an outstanding mailpony who should not doubt herself.
In Chapter 20, he rewards her performance by offering an extension to her route - specifically, Fluttershy's cottage - and correcting her unjustly low place in the pay scale from Cloudsdale, resulting in a 35% raise.
Never before would she have imagined that she would be commended for her ability, given more responsibility, and rewarded with a substantial raise. She couldn’t comprehend even getting one of those results, but having all three happen simultaneously left her utterly speechless.
Derpy: I… I don’t know what to say. I can’t even begin to describe what this means to me. I’ve never been rewarded like this for anything before. I just hope I don’t let you down. I’ll do my best to meet your expectations.
Post: I’m sure you’ll meet them and more, Derpy. You’ve exceeded my expectations more than you know, and, to be honest, you’re the most dedicated mailpony I’ve ever hired. You deserve recognition for that – I’m just sorry that it took so long for you to receive it.
In Chapter 16, Rainbow Dash resolves to let go of her long-standing grudge against Derpy upon realising that she's basically what Fluttershy would have been had she not had Rainbow Dash for support. The following chapter has a particularly moving apology from her:
Rainbow Dash: I’m sorry for everything that I’ve ever done to you, since the day I first met you. I never gave you a chance, I never got to know you, I just joined in the crowd making fun of you, and it’s only gotten worse since. You never deserved any of it, and if I had only stood up for you, your life may have been so much happier. That’s why I’m sorry, and why I’m asking for your forgiveness. I’m apologizing for years of undeserved misery for you that I’ve been an eager part of.
After some hesitation, Derpy hugs her.
Derpy: Rainbow Dash, I accept your apology, and I forgive everything you’ve done. It’s not easy for me to forget the past, but the past does not need to be forgotten to be accepted, and it does not need to be ignored for us to move on.
In Chapter 22, Derpy reassures Fluttershy that Mr. Zippy and the other mailponies don't resent her for her post-Iron Will behaviour.
While Celestia's letter to Twilight in Chapter 24 ends on very bad news, she warmly congratulates Twilight on her newfound love and makes it clear that she takes no pleasure in forbidding her to use the exotropia spell again.
Twilight and Derpy's reconciliation after the former tore up the library when her magic got out of control due to her anger at Celestia and almost injured the latter.
From the same chapter, Derpy reveals that she's come to accept herself for who she is, at which point the last of her Cutie Mark bubbles changes colour, to grey with a blonde edge.
Derpy: It’s not a big deal. In fact, it doesn’t matter at all – I’ve never been happier than I have been after meeting all of you, regardless of what my eyes have been like. I don’t need my eyes to get better. I just need you girls for friends.
The epilogue. Twilight and Derpy have gotten engaged.
