How the does the ending of Harper Lee's To Kill a Mockingbird show us how Scout's perception of Atticus has changed?
Perhaps what changes most about Scout's perceptions of Atticus by the end of Harper Lee's To Kill a Mockingbird is how fragile an individual he is when his children are in danger.
Atticus can take on Aunt Alexandra, though she does frustrate him when he has to choose between supporting his sister and defending his children. He is unafraid of Bob Ewell, who threatens him after the trial. When he spits on Atticus, Atticus does not take offense. He casually notes:
I wish Bob Ewell wouldn't chew tobacco...
When Cunningham and the other men come to lynch Tom Robinson, Atticus is fearful for his children, but he is able to handle it so that Jem and Scout aren't shaken by what Atticus sees as a potentially dire situation for them. (And he understands the mob mentality, as well.) However, the event in front of the jail that night foreshadows Atticus' complete devastation in face of how closely he comes to losing his children.
As Boo (we later learn) carries Jem across the yard and into the house, Atticus runs down the stairs. Atticus doesn't ruffle easily; even when shooting Tim Johnson, the rabid dog, Atticus paces himself. When it comes to his children, his self-possession is gone.
Carrying Jem into his bedroom, Scout recalls her father speaking:
"Call Doctor Reynolds!" Atticus' voice came sharply from Jem's room.
When he asks after Scout, we can imagine his voice is also tight with worry. Atticus comes out of Jem's room and immediately asks Eula May (the town operator) to get the sheriff. By now, the mood has been established regarding Atticus' frame of mind. He tells Heck straight out:
Someone's been after my children...I can't leave my boy.
Atticus wants the perpetrator caught, and Jem is obviously safe, but we can infer Atticus' level of concern...for he refuses to leave Jem.
We can also sense Atticus' state of mind in that when Scout asks if Jem is dead, he does not stop answer her in detail. He responds with a quick "No, Scout" and asks Alexandra to look after his daughter. Atticus has always taken time to comfort and/or provide explanations, but now he has to be with Jem.
Once again, Scout sees Atticus in a new light when he hears not only that Bob Ewell was involved (which bears out Ewell's earlier threat against Atticus), but also that he is dead. Atticus forgets to exercise good manners and stand when Aunt Alexandra is overcome with emotion (though Heck Tate does get up)...
For once in his life, Atticus' instinctive courtesy failed him: he sat where he was.
Atticus speaks to Heck "bleakly." Scout notes...
His age was beginning to show, his one sign of inner turmoil, the strong line of his jaw melted a little, one became aware of telltale creases forming under his ears, one noticed not his jet-black hair but the gray patches growing at his temples.
In face of a lynch mob, Bob Ewell's hatred directed at him, Mrs. Dubose's censorship, and the town's overwhelming disapproval for taking Tom Robinson's case, Atticus never batted an eye. Confronted with coming to close to losing his children, Scout begins to see that her father is really human after all. Certainly she considers him feeble and "old," but she has never really noticed before signs of age in his face; his age was a perception based on how she saw him. Perception meets reality as she recognizes the emotional toll on her father—for this is most likely the only thing that could harm him—even more than violence carried out on Atticus himself.