One of the more significant examples of dramatic irony--a contradiction between what a character thinks and what the reader or audience knows to be true--is Amanda's remark to Tom in their final dialogue:

"Go, then!  Then go to the moon--you selfish dreamer!"

Of course, the irony here is that in many respects, Amanda is both selfish and a dreamer herself.  For all her concern about Laura and Tom, at the heart of this concern is Amanda's desire to secure her future.  If, for instance, Laura marries a gentleman caller, then Amanda can be taken care of in her old age.  Likewise, if Tom continues to support the family and not abandon them as his father has, Amanda will also be safe. She is not concerned about Tom's artistic desires; she simply wants him to serve his sister and her. 

That she is a dreamer is clearly evinced in Scene 6 when Amanda attends Laura's dressing as thoug it her wedding dress that she ceremoniously alters for her daughter.  The significance that she places upon this visit from one of Tom's friends is also unrealistic.  For example, she interrogates Tom about Jim O'Connor, wanting to know his name, what he looks like, what his salary is, if he drinks, if he has character, etc.  Then, when Jim arrives, Amanda greets him in the voice of a Southern belle, sweeping Jim away with her "gay laughter and chatter." Besides, she is dressed as in her youth, shocking Tom at her appearance.  And, yet she tells Laura in at one point in the scene, 

"Fantastic whim and behavior. Preposterous goings on!"