What versions of the clients do you use? I only get this error on my Linux client. OS X, Windows, iOS and Web are looking fine. All desktop clients are 1.3.0 (most current).
Also, do you get a "We received an unexpected status code from the server. (404)" too at the top of the client, and the status icons have disappeared?
My nginx config is very similar, and, as most of my clients do work fine, i don't think it's an nginx problem at all.
I most likely will open a support case as we use the enterprise version. Hope they will answer quicker then...