I wanted to document this error here because I recently went nearly blind trying to solve it, and I never did find the exact cause when Bing'ing for it. Unfortunately it's a pretty generic error so it may very well have been out there, but it seems there are several reasons for it. In my case I created a new instance of a class that I was adding to my Azure table but it kept failing with this "One of the request inputs is out of range" error that was driving me absolutely nuts. Fortunately some bright individual pointed out to me that my class contained a DateTime property, and I wasn't initializing it. Apparently the default DateTime.MinValue in .NET is outside the bounds of what Azure table storage supports. So I just put in a dummy date in my property and - voila! - everything started working again.
So just a heads up in case you see this error yourself - it seems like a pretty easy one to miss.
Hope everyone has a happy holiday season!