Bob Ewell's point of view is discussed in chapter 23. Atticus mentions this in the first few pages of the chapter:
Jem, see if you can stand in Bob Ewell's shoes a minute. I destroyed his last shred of credibility at that trial, if he had any to begin with. The man had to have some kind of comeback, his kind always does. So if spitting in my face and threatening me saved Mayella Ewell one extra beating, that's something I'll gladly take.
Obviously, Atticus understands who Ewell is and why Ewell would act the way that he did.
In chapter 11, Mrs. Dubose called Atticus a nigger-lover when speaking about him to the children. The kids took offense, but Atticus told them:
... don't let Mrs. Dubose get you down. She has enough troubles of her own.
Here, readers see Atticus able to see the world from Mrs. Dubose point of view. Some of the troubles she had were being from a different generation and dealing with the condition of being old and fragile.
Finally, in the last chapter Scout sees the world from Boo Radley's vantage point. The entire chapter demonstrates his viewpoint, so most any quote would prove Atticus' theory. Scout recounts the events of the entire book on Boo's front porch as if she was view. It seems to be a moment in which Scout finally believes Atticus' teaching that its important to see the world from a variety of perspectives.