What evidence does Atticus bring out that discredits Bob Ewell's story?
There are several points that Mr. Finch elicits from witnesses that discredit the testimony of Bob Ewell.
Even before Bob Ewell takes the witness stand, Sheriff Tate testifies about Mayella's injuries. He reports on his being called by Ewell and what he saw when he arrived. Tate states that Mayella was bruised on both arms, and her right eye was blackened. Also, Tate testifies that Mayella had apparently been choked because there were finger marks on her neck. Atticus Finch asks the sheriff the following:
"All around her throat? At the back of her neck?"
"I'd say they were all around, Mr. Finch."
The fact that Mayella's neck was bruised with finger marks all around her throat indicates that someone used both hands to choke her. And, the blackened right eye suggests that Mayella Ewell was hit by someone's left fist. Anyone who knows Tom Robinson knows that Tom Robinson's left arm is withered and rendered useless as is his lifeless left hand. Therefore, if Tom were the one who choked Mayella, marks would only be on one side of her neck.
Further, when Bob Ewell testifies, he claims that he heard Mayella screaming "like a stuck hog." When he ran into the house, he further alleges, Mayella was lying on the floor "squallin.'" Ewell also states that he left her and ran for the Sheriff Tate "quick as I could." Therefore, he neglected to make certain if she were injured badly at all. He also states that he did not call for a doctor. These admissions of Ewell's suggest that he has exaggerated his testimony.
There are two pieces of evidence that discredit Bob Ewell completely and they have to work together. First, Atticus shows that Bob Ewell is left-handed, and Bob tries to show that he can use both hands, but it's too late. Then, when he asks Tom to rise after Mayella pointed him out, the courtroom sees the other necessary piece of evidence: Tom's left arm is 12 inches shorter than his right.
This proves it would have been impossible to leave the injuries on Mayella that were there. It also leaves the question on the table, if not Tom who? The fact that Bob was left-handed proved that it was possible he beat his daughter because the person who hurt her led exclusively with his left.
There are two main things that Atticus brings out that I think are important.
First, he brings out the fact that Bob Ewell is left handed. He shows that Mayella was almost certainly beaten by someone who was using his left hand.
Second, he brings out that Ewell does not call for a doctor. He says that this shows that Ewell knew Mayella had not been hurt by Tom Robinson. If she had, he would surely have called a doctor.