In Chapters 2 and 3, Derpy's breakdown while talking with Twilight, after the latter knocked her over and scattered her bag of mail during a rainstorm.
Twilight: I am very, VERY sorry about that, by the way. I guess I never realized how much you cared for your work; you must be very proud to be able to give such a service to everypony around.
Derpy: Proud? I’m not proud; I never have been and I never will be. I’m a failure, Twilight. A disaster waiting to happen. I’m the outcast with messed up eyes and a featherbrain, and the only time ponies will stay around me is when they want a front seat to the next catastrophe I’ll cause. I’m less than a nopony; noponies don’t destroy town halls, demolish mail shipments, or drop pianos on other ponies’ heads. Twilight, the reason I was down here doing my deliveries today was that I screwed up in Cloudsdale yesterday, too. I was sent here as a sort of initial demotion. After today I may not even have a job anymore, and all I’ll be is the comedic relief; the pony other ponies point and laugh at every time she falls, every mistake she makes. All that’ll be left is the… the featherbrained disaster with messed up eyes.
In Chapter 7, Derpy's story about how much she lost after her eyes started to cross, seemingly too late to do anything about them.
In Chapter 22, Twilight sends Princess Celestia a letter informing her of her relationship with Derpy, details about her incomplete Cutie Mark and the spell that she found to fix her wall-eyes. In Chapter 24, Celestia responds by admonishing her for risking her marefriend's safety and informing her that the spell has, as a result of her research, been forbidden by the Equestrian Medical Association.
It gets worse in the next chapter, when Twilight's anger, along with her magic, gets out of control, and she destroys much of the library, causing injuries to Spike, Rainbow Dash and Applejack, the latter of which was trying to protect Derpy.
