Steven Pinker included this entertaining clip from a "movie script" in one of his books:
Woman: I'm leaving you.
Man: Who is he?
This is one of my favorite examples of the truism that a lot more is going on in language than meets the eye. To understand this dialog, one has to make a number of assumptions. More broadly, to understand it, one has to know a great deal about human behavior. Imagine a computer programmed to understand language but which knows nothing about humans. How would it interpret this scene?
This is my primary area of research, so if you are interested, check out my blog. I am also running a couple experiments online trying to work out some of what's going on in language. You can find them here.