In To Kill a Mockingbird, what did Atticus say in his closing argument that helped his case and what did he say that didn't?

The worst about the Tom Robinson case overall is that it is based on hearsay and racsim. A case like that should never have gone to trial because there were no secondary witnesses or evidence to support the Ewell claims. The only reason it did go to trial is because a white man accused a black man in Alabama in 1935. Atticus does his best to provide the best defense for Tom, but even he knows the odds are stacked against him from the get-go. After a grueling trial, Atticus gets up for closing arguments and does a fabulous job reviewing the findings of the case. The best argument that supports the defense goes as follows:

"The state has not produced one iota of medical evidence to the effect that the crime Tom Robinson is charged with ever took place. It has relied instead upon the testimony of two witnesses whose evidence has not only been called into serious question on cross-examination, but has been flatly contradicted by the defendant" (203).

During the trial, Atticus proves that Mayella was mostly beat up on the right side of her body, which would have been done by a left-handed man. Atticus proves that Mr. Ewell is left-handed and Tom's left arm is mangled; therefore, Tom couldn't have beat her up. That alone should have ended the trial. 

What didn't help Tom's case, though, is when Atticus points the finger at Mayella Ewell and calls her the guilty one. However true this may be, this is irrelevant because Mayella isn't on trial. All Atticus needed to do what cite the evidence and prove his client innocent. If he wanted to go after Mayella, he would have had to file a counterclaim. Atticus says the following:

"The defendant is not guilty, but somebody in this courtroom is. . . I have nothing but pity in my heart for the chief witness for the state, but my pity does not extend so far as to her putting a man's life at stake, which she has done in an effort to get rid of her own guilt" (203).

Clearly, Atticus is taking this chance to teach a long-delayed lesson to the people in his community, and to the Ewells, but it is unnecessary and does not help the case. He is appealing to the Jury's sense of right and wrong, though. He is trying to get them to think a little bit deeper into the real issues at hand. Sadly, when talking to an all-white-male jury in twentieth-century Alabama, it's not going to do much good for a black man's case.