The Two Dysarts
In this play, Martin Dysart exists in two forms: as the narrator, who tells this story in retrospect, and as himself within the story, actively treating Alan. Since the audience is introduced to the narrator Dysart from the very beginning, there is a sense of dramatic irony as we watch him agree to take on Alan, since we know how profoundly affected he will be in the end by his experience treating him.
The Parents' Blaming of One Another
The way that both Frank and Dora constantly try to implicate the other for causing Alan to turn out like this is ironic, since it is clear that both of their child-rearing methods have played a significant part in shaping Alan into who he is. Neither is completely innocent in this situation, yet both vehemently claim they are.
Pain is Good
Dysart's claim that Alan's pain is a good thing is ironic, since the pain is typically conceived of as extremely negative. He argues that Alan's pain stems from an intense passion that defines him, and insists that this pain is a worthy trade-off. He himself expresses jealousy that Alan is able to achieve such a level of worship, because he wishes he had that kind of worship in his own life.
The Therapist is Transformed
The point of therapy is to transform the client in some way. In this play, however, it the therapist himself has been transformed even more than the patient. Treating Alan has brought Dysart to a new level of self-doubt and uncertainty, and in the end he feels like he has taken on Alan's pain and feelings of confinement.