What is the overall significance of the story's extensive use of animal symbolism?
I am not aware of much animal symbolism in A Good Man is Hard to Find. I looked the story over and just found the mother being described like a rabbit because of the hankerchief on her head. Also, the grandmother carries the cat, they find a monkey at the service station, and the Misfit says he's the same breed of dog as his brothers and sisters. Any animal reference could go along with the fact that O'Connor views the characters with detachment. She does not give the reader characters they can get connected with, and this style increases the dark and ironic tone of the work.
I would add that the animal motif suggests O'Connor's fascination with the grotesque. Many of her stories, including "Good Man," are concerned with our flawed nature as a result of orginal sin, a fall from grace. Using images that show her characters as bizarre in appearance, which is an aspect of the grotesque, is one way of communicating this theme.