I see how to set headers for GET and POST, but how do I get the headers on the response? There's data there that I need to read.
We added support for responseheaders to the WWW class in Unity3.
You can't with the default WWW implementation. You'd have to go through the .NET web client class most likely:
http://msdn.microsoft.com/en-us/library/system.net.webclient(VS.80).aspx