Question about the last few lines of To Kill A MockingbirdIn the last few lines of To Kill a Mockingbird, Scout says, "He was real nice..." and...

Atticus's ability to "see the good side of people despite
all he has experienced" is a direct result of his respect for all human
beings. 

Early on in the novel, Atticus tells Scout, "you
never really understand a person until you consider things from his point of view--until
you climb into his skin and walk around in it."  Essentially, Atticus believes--and
tries to teach his children--that in order to really understand a person's motives,
behavior, or words, one must be able to see things from that person's perspective. 
Though this advice seems simple and logical, many people, including most of the citizens
of Maycomb, fail to take the time to practice this exercise in
tolerance.

With regard to your first question, I think that
the children are ultimately able to understand that most people are good people.  They
understand that Mrs. Dubose, while mean and abusive in her language, is a courageous
woman; they learn that Mayella, though she accuses Tom of Rape and wrongfully puts him
on trial for his life, is a sad, lonely, and abused girl; they learn that Dolphus
Raymond, the town outcast, is not what many citizens of Maycomb describe him as; and
perhaps most importantly, they learn that Boo Radley, their "malevolent phantom" of a
neighbor, is a nice person.  (The exception to this response, I'd say, is Bob Ewell.  He
doesn't show any redeeming qualities in the novel.)

More
important than the specific examples listed below are is the knowledge the children gain
from learning to put themselves into others' shoes in order to gain insight and
perspective into the life of another person.  Essentially, Atticus strives to teach his
children empathy and compassion for all others.