Your question says "political injustice"; is this being equated to social injustice? If the question is truly about political injustice, then Atticus Finch is on the receiving end as his having to defend Tom Robinson could be costly to his career if he wishes to run to county or state office. For, he has Mrs. Dubose and others vilifying his character with name calling and such.
I must admit, when I first read this novel (many moons ago), I was struck by the way in which Boo Radley was unfairly treated more than other characters. However, as other posts above point out, it is clear that the novel presents us with many different examples of injustice, and I guess you need to pick the one that resonates with you most strongly.
I think that one could look at Boo or at Tom. Both face social injustice based upon either prejudice (Tom) or the unknown (Boo). Boo faces injustice based upon the fact that people are judging him based upon lore. Tom faces injustice based upon the fact that he is black. Outside of those reasons, neither man should face the discriminations society looks upon them with.
I think you could also look at Boo Radley. We don't know what of his past is true and what is town folk-lore, but he clearly has had a troubled past in his youth. As a means to handle him, his brother keeps him shut away from the people in the town, but he clearly does pay attention to the happenings outside his window: he finds and mends Jem's pants; he puts a blanket around Scout the night of the fire; he leaves treasures in a tree for the children; and he runs out the dark of night to stop Bob Ewell from harming the children. He copes to the injustice of being held prisoner in his house by doing what he can to have outside connections.
Tom Robinson is the most obvious character here, but you might also consider Dolphus Raymond. He is a person who has been persecuted for the fact that he chooses to love a black woman. He overcomes this to some extent by pretending to be a drunk. By doing so, he shields himself from other whites' disapproval of his social life.
In reply to #4
I found Dolphus Raymond the most interesting character in the book since he found a way to overcome the social injustice in his own peculiar way.
The biggest political injustice is committed against Tom Robinson, who is falsely accused of rape and put on trial. He is convicted when there is no way he could physically commit the crime. Tom chooses not to appeal, but rather to run for the prison fence. This is suicide, because with one arm he doesn't stand a chance. However, Tom is overcoming his obstacle. He ended things on his own terms, and used the only power he had.
Thank you for your post. I concluded somewhat the same on this subject.