Atticus displays many positive aspects of his To Kill a Mockingbird character as well as his parenting skills during the chapters concerning the mad dog and Mrs. Dubose. Atticus apparently has pledged to never pick up a gun again following his earlier life as "One-Shot" Finch. But when he sees that he is the best man for a dangerous job, he rediscoves his deadeye aim once again, dispatching of Tim Robinson with a single shot to the head. However, Atticus does not want his children to know of his earlier skills, and cautions Sheriff Tate to "hush." He is not proud of his skill to kill, but the children soon learn the truth from Miss Maudie, who explains that "people in their right minds never take pride in their talents." Atticus' actions display the humility that is part of his makeup.
When Jem destroys Mrs. Dubose's camellias, Atticus lets Jem know that his display of destructive temper is not acceptable--no matter the insults tossed by the old woman. Jem is taught a lesson through his punishment, just as Atticus expects. He knows the true story behind Mrs. Dubose's request for Jem to read to her, but he thinks it best not to tell Jem until after her death. As uusual, Atticus does not mince words with Jem, and the realization of Mrs. Dubose's morphine habit, coupled with the gift that she has left for him, is almost too much for him to accept. But Atticus wants Jem to learn from his time spent with her, and his parental wisdom is just and appropriate.
In To Kill a Mockingbird by Harper Lee, Miss Maudie explains the lesson to be learned about the character of Atticus Finch in these two incidents much better than anyone else as she tells Jem and Scout,
If your father's anything, he's civilized in his heart.
Miss Maudie explains that because Atticus had such a talent in shooting, he felt that God had given him an unfair advantage over most living things: "I guess he decided he wouldn't shoot till he had to, and he had to today."
Likewise, Atticus is not cruel in the courtroom until he has to ask certain questions in order to obtain the testimony necessary to acquit Tom Robinson. Nor, does he retaliate against Mrs. DuBose for her pejorative remarks about him, knowing that he would again have an unfair advantage over the gravely ill old woman.
When we see Atticus deal with the mad dog and with Mrs. Dubose, we get more of an insight into his character.
When he shoots the mad dog in Chapter 10, we find out that he has a very strong nerve. Here is a man who used to be a great shot, but that was 30 years ago. Now he has to take a shot at a dangerous dog where if he misses the dog might bite someone and the bullet might go into the Radleys'. The fact that he hits the dog shows that he has strong nerves.
From Mrs. Dubose, we see that Atticus is very tolerant and can even learn from people who treat him very badly.