First, the title itself is ironic: "The Green Door" is about a young man's sense of adventure leading him to knock on a green door, but, the card that is handed to him by the ornate man advertises a play entitled "The Green Door." The irony lies in the contrast between what is expected by the title and what one reads in the narrative and what happens when the young man actually opens a green door instead of attending a play of the theatre. Added to this, there are several green doors!
Secondly, there are subtle ironies in the story that set the reader up for the biggest One such irony is in the contrast of what the reader expects O. Henry to write and what he actually does when he puts "while you are choosing between a diverting tragedy and something serious in the way of vaudeville. [Comedy, not tragedy, is diverting; vaudeville was anything but serious.] Another example of an ironic statement is "A fine example of a true adverturer is the Prodigal Son--when he started back home." [How was it an adventure to return home?] Still another example or irony is O. Henry's statement that the starving girl "approved of his bereft condition." [Why would she think it good that the man, too, is without things?] And, the final irony under irony of the title is the multiple green doors, yet the adventurer feels Fate brought him to the particular door. [Do not adventurers hold with pure chance, not any kind of Destiny?]