1. Towards the end of chapter 15, when the angry mob comes to the jail to harm Tom Robinson, Scout and Jem happen to be there. Scout, being a child, doesn't understand the full extent of the dangerous situation. In her innocence, she recognizes Mr. Cunningham as one of the men there, and asks innocently,
"Hey Mr. Cunningham. How's your entailment gettin' along?...I go to school with Walter...and he does right well. He's a good boy."
She is casually making conversation with a man who has come to injure and possibly kill an innocent black man. She doesn't quite understand the situation. And, she is confused as to why he isn't responding to her, or being kind. She narrates,
"Atticus had said it was the polite thing to talk to people about what they were interested in...So I tackled his entailment once more in a last-ditch effort to make him feel at home...I was slowly drying up, wondering what idiocy I had committed...'What's the matter?' I asked."
She feels awkward that everyone is just staring at her, and innocently asks them what is going on. This instance of childhood innocence saves the day; it forces Mr. Cunningham to act as a decent, human being instead of an angry mobster. He takes the mob and leaves--Scout's innocence put a face on the mean thing these men were going to to, and gave them a perspective check.
2. In chapter 12, after Scout and Jem go to Cal's church, Scout is amazed at the fact that Calpurnia has a life outside of the one that she lives with them. In her childhood innocence, she doesn't realize that Cal doesn't belong only to their lives, and has other situations going on. Kids are very self-focused, and understand the world only as it relates to them. She states,
"That Calpurnia led a modest double life never dawned on me. The idea that she and a separate existence outside our household was a novel one, to say nothing of her having command of two languages."
3. Scout asks question after question that reflects her naivety and innocence. One is that she asks Cal, "What's rape?" Another one is when she asks,
"Cal,...why do you talk nigger-talk to the--your folks when you know it's not right?"
Another is when Walter is pouring syrup on his food, she states,
"he would probably have poured it into his milk class had I not asked what the sam hill he was doing."
All of these questions reflect a childhood's innocent nature, one who doesn't know more adult and mature things in the world.
I hope that these thoughts help a bit; good luck!