1) Scout sees the gang, and notices Mr. Cunningham is part of it. She talks to him about his son, Walter Jr., who is in her class and has been to their house at lunch time. When she speaks to Mr. Cunningham, it reminds him that he is threatening someone who is a father, just like he is. It also reminds him that he has ties in the community, and it wouldn't be right to break those ties violently. After this, the rest of the mob begins to feel badly about their purpose at the jail, too, because they are not quite sure of it enough to be violent in front of a child.
2) People dislike Dolphus Raymond because he came from a respectable, white family and ended up with a black mistress. Most white people could not understand why he would prefer the company of black people; to help them with this, he pretended to be the town drunk. That way, if people thought he was drunk, they would assume he was acting strangely because of the liquor and not because it was his choice to do so.