Also in both stories the main character is a woman who is smug in her convictions of superior importance. One of O'Connor's aims is the puncture the swollen self-estimates of such people. The irony between what such a person is and what the woman assumes herself to be is emphasized by such techniques as unflattering names (Turpin suggests moral turpitude.) or appearance (The grandmother insists on dressing carefully so that "in case of an accident anyone seeing her dead on the highway" would know she was a lady; ironically, after the wreck, her hat begins to disintegrate.)
Both stories contain violence, another motif often used by O'Connor to shock her characters (and the reader) into an epiphany. Mrs. Turpin is physically assaulted by Mary Grace, first by the book thrown at her and then by the girl's attempt to strangle her; the grandmother hears the gunshots that kill her family one by one prior to her brief epiphany before she, too, is murdered.
The most obvious would be in the theme. Flannery O' Connor frequently wrote about grace, redemption, and salvation (these two stories contain characters who have epiphanies, as well). Both of these stories contain themes of grace, redemption, and salvation. Mrs. Turpin receives her realization about grace and salvation through Mary Grace; whereas, the grandmother in "A Good Man..." receives her realization about grace and salvation through the Misfit.
Other similarities include setting (O'Connor can be classified as a regional writer, much like Faulkner) and similar main characters (Mrs. Turpin and the grandmother).