The moments of comedy in this play are perhaps related to the way in which Blanche persistently lies about her alcoholism and pretends that she doesn't have a problem when she absolutely does. Of course, it is clear that she is not able to kid Stella and Stanley, and she repeatedly makes reference to the fact that she doesn't drink too much even when she obviously does, saying things like, "No, one's my limit" and constantly trying to explain away her actions, as in the following quote:
Now don’t get worried, your sister hasn’t turned into a drunkard, she’s just all shaken up and hot and tired and dirty!
Of course, when she is trying to flirt with Mitch there is a very humorous speech where she obviously slurs her words because she has drunk too much:
I’ll show you shuperficial--Listen to me! My tongue is a little--thick! You boys are responsible for it. The show let out at eleven and we couldn’t come home on account of the poker game so we had to go somewhere and drink. I’m not accustomed to having more than one drink. Two is the limit--and three! [She laughs] Tonight I had three.
The humour in this passage actually reveals her own weakness and her desperate situation. To try and fit her Southern belle persona, she is not able to admit that she has a problem with drink and so constantly has to lie about her drinking habits, even when it is obvious to everybody that she has a problem with alcohol.