We know there is a man in the middle vulnerability with unauthenticated DH key establishment. And the way to negate that is to use authenticate the keys used. But what if I only verify the signature of one end. Is there any vulnerability then?
EDIT: To be clear, I am not referring to the fact that the authenticated party does not know who its talking to. I am specifically thinking about a cryptographic vulnerability where someone who does not have control over the machine (of the unauthenticated end) can do some damage.