In To Kill a Mockingbird, during the court testimony about Mayella's injuries, what key facts seem inportant to Atticus.
In Harper Lee's To Kill a Mockingbird, Atticus is very careful regarding the testimony about Mayella Ewell's "injuries." He is very concise when questioning Heck Tate, the sheriff, and even thorough in his cross-examination of Mayella Ewell and Bob Ewell.
The significance of this is to establish the veracity or truthfulness of what the Ewells are accusing Tom Robinson of. This speaks to two different concerns on Atticus' part. First, Atticus already knows that Tom has one arm that is useless to him caused by an accident with a cotton gin when he was younger. In connection with Tom's inability to harm Mayella based on the side of the face that was damaged, is the question of Bob Ewell—not only is he his daughter's real attacker, but whether he has an abusive nature in general as a father?
First Jem notices the strategy Atticus is using by asking questions about Mayella's life.
Atticus was quietly building up before the jury a picture of the Ewells' home life.
Later, Atticus asks Mayella what kind of father Bob Ewell is.
"I mean, is he good to you, is he easy to get along with?
"He does tollable, 'cept when—"...
"Except when he's drinking?" asked Atticus so gently that Mayella nodded.
When Atticus questions Tom Robinson, we learn that Mayella made advances toward him, not the other way around. She kissed him because she wanted to know what it was like: besides the "kissing" from her father.
"She said she never kissed a grown man before an' she might as well kills a n***er. She says what her papa do to her don't count."
(Here is an inference, based on Tom's testimony, that Mayella may also have been sexually abused by her father.) Tom then explains that when Mayella's father saw what she was doing through the window, he went berserk.
"I didn't wanna harm her, Mr. Finch, an' I say lemme pass, but just when I say it Mr. Ewell yonder hollered through th' window."
"What did he say?"
Tom Robinson swallowed again, and his eyes widened. "Somethin' not fittin' to say—not fittin' for these folks'n chillun to hear—"
"What did he say, Tom? You must tell the jury what he said.
Tom Robinson shut his eyes tight. "He says you goddamn whore, I'll kill ya."
Jem reports that Tom Robinson's manners were nearly as good as Atticus'. As Atticus reports later, Tom tries to get away without pushing Mayella, for…
...if he dared to strike a white woman under any circumstances [he could not have expected] to live long.
However, by running away, it also made Tom look guilty—Tom faces a serious predicament. There is really no way he can come out of this situation unscathed.
All of this information points to Atticus' intention of establishing that Tom had no use of his left hand, that Bob Ewell was left-handed (and probably hit Mayella), that Ewell was violent when he had been drinking, and that he threatened to kill Mayella for kissing a black man. Atticus is trying to develop a case that clearly demonstrates Tom's inability to carry out the deeds he is accused of, and therefore, his innocence, and Bob Ewell's guilt in the beating of Mayella, and lying in court.
in addition to @booboosmoosh 's answer, proof that Mayella's father has done things to her before, Tom Robinson states,
She says she never kissed a grown man before an' she might as well kiss a n***er,. She says what her papa do to her don't count.
therefore stating that Bob Ewell has done things to her.
she was beaten on the right side of the face