Though the violence and talk of rape in the novel can be upsetting, the most obvious answer is probably the use of the "n" word. To avoid or ignore it however, in a novel intended to expose racism, particularly in the American south of the 1930s, would be to create a less-than-truthful foe. The dragon would be toothless. And when Scout uses the word, she is immediately admonished by Atticus "Don't say 'nigger' Scout. It's common." Scout's naivete in not realizing the harmfulness of the word (she merely repeats what she has heard classmates and Maycomb townsfolk say) adds to her verity as an impartial observer of the events in the novel. She speaks the truth as she sees it.
Apparently the objections to the book include the use of profanity and the violence, especially rape. The eNotes link below will take you to an article about this very topic, which also says that initial responses against the book came from the South, where people felt that whites, and their treatment of blacks, were portrayed in a poor light. Unfortunately, the fire spread and the book was attacked by people across the U.S. for the aforementioned reasons.
Personally, I would think that a careful reading of the book would demonstrate that Miss Lee actually showed the good and the bad in her portrayal of the white citizens of Maycomb, Alabama. In addition, her treatment of the rape trial and the language she chose was appropriate to the story of what two young children experienced during critical growing up years.