From your logs it looks like the automatic updater program we use, wyUpdate is complaining about its settings file, client.wyc. Perhaps this file is corrupt. If you wish, please email us the client.wyc file and we'll look into it.
Version 0.55 is pretty old, but we haven't changed the format. You should be able to update to the latest version from it, but we haven't tested it. You can always install the latest version over the old version. Just download syncdocs.msi from download page and install it.
Regarding the 400 and 503 errors reported by Google in your log, these often occur when one of the two users don't have the permission to access the files.