In "A Good Man is Hard to Find," the thematic irony is built around the disparity between the grandmother's view of herself and the reality. She feels that what defines a "good man" is the kind of family that they come from and the way that they dress. Note what she says to the Misfit after she has identified him:
I know you're a good man. You don't look a bit like you have common blood. I know you must come from nice people!
The grandmother defines a good person by the kind of family that they come from, yet ironically she is blind to the tremendous prejudice that lies within her. She comes to realise by the end of this story that it is her prejudice that links her to the Misfit, although her sin is in a different league to his misdemeanours.
In the same way, irony is present in "The Birthmark" through Aylmer's obsession to "cure" his wife through erasing the birthmark that lies on her cheek. Note what he says to her as he comments upon her blemish:
Georgiana, you have led me deeper than ever into the heart of science. I feel myself fully competent to render this dear cheek as faultless as its fellow, and then, most beloved, what will be my triumph when I shall have corrected what Nature left imperfect in the fairest work!
To Aylmer, he is unable to view his wife's birthmark as anything but a "blemish" or an imperfection of nature needing his help to erase it. Ironically, he is unable to love his wife for who she is, warts and all, and as a result only succeeds in his goal at the expense of killing his wife. Thematic irony is present in both tales through the lack of awareness of the protagonists of their actions and how they impinge on other people.