Atticus strongly believes in the goodness of the American system of justice, but he is no idealist. He says in Ch. 23: "The one place where a man ought to get a square deal is in a courtroom, be he any color of the rainbow, but people have a way of carrying their resentments right into a jury box." Although the verdict was wrong and unjust, Atticus still says the news wasn't all bad because at least the jury took its time rather than returning a verdict immediately, and that for him was proof that at least one person on the jury was doing some thinking--that being Mr. Cunningham. Thus, for Atticus, it's almost a game of numbers--if the jury had just one more person like Cunningham, the verdict might have gone the other way. Finally, Atticus seems to think it's a good thing that women were not permitted to sit on juries. He smiles when he says this, but it does indicate some of the issues concerning "southern ladies" in the novel.
Atticus believes that for a person to be sentenced to the death penalty, there should be one or two witnesses to the crime. He doesn't believe its fair to convict on circumstantial evidence. Atticus also believes that when a conflict comes down to race, men lose their heads and are no longer reasonable and rational. He defines 'white trash' as the men who as they grow older grow more bitter and cheat black men.
As whites, the society of Maycomb is automatically given a status superior to all African-Americans based on simply the color of their skin. This power is distributed unfairly: the character, the moral values this person holds mean nothing whatsoever to determine whether this person should be given this privilege. What Atticus has continued to explain throughout the novel is that he is extremely disgusted with anyone who, for their selfish needs, will misuse this privilege or power over the powerless African Americans who have no voice in society: no hope of change, and no choice as to decide who they will be.