One of the most important themes of this story has to do with the problems that arise when a person continues to hold on to antiquated ideas and prejudices. The narration is third-person limited omniscient (for the vast majority), focusing on the thoughts and feelings of the grandmother, an older woman who is very much attached to old-fashioned ideas about what it means to be a "lady" or to be a "good man." As a result, we learn things like her belief that she should dress prettily for the road trip so that "in case of an accident, anyone seeing her dead on the highway would know at once that she was a lady."
No one in her family seems to respect her or her ideas—she clashes with her son and her grandchildren throughout the story. One of the first things she says to the Misfit once she identifies him is, "'You wouldn't shoot a lady, would you?'" And she goes on to say that she knows he's "'a good man. You don't look a bit like you have common blood.'" He eventually says, "'Nome, I ain't a good man.'" At least, by the grandmother's standards he's not. If he weren't threatening her, she probably would think he is common, and it was probably people like her who put him away for a crime he didn't commit. She's only telling him he's "good" so that he won't shoot her.
After he shoots her, he tells his friends that "'She would of been a good woman . . . if it had been somebody there to shoot her every minute of her life.'" Her idea of what makes a "good" person is outdated: it isn't about having good manners or being more than "common"; it's about being compassionate and kind (as she is in the moment just before she dies). Being a "lady" in the old-fashioned sense isn't really important anymore. Being the type of person who recognizes the humanity of all people, no matter how different from you they might seem, is what makes someone a "good" person. In the end, when the grandmother suddenly sees the Misfit as "'one of [her] babies,'" she has this moment of clarity, this epiphany where she sees what she and the Misfit have in common rather than how they differ, and this is the "goodness" that she develops only as a result of having a gun pointed at her.