Updated phone app and still get the message from desktop client that I have an outdated version

@nettics
Try uninstall AirDroid app on your laptop and install again

I had the same problem.
@nettics suggestion did not work, although it was a good example of the idiom "taking a shot in the dark".

I found my problem to come from a "proxy server" called Privoxy I installed on my laptop to speed up the browser on an old Logitech Revue GoogleTV box, and was able to configure it to ignore html requests going to .privoxy.

If you have no idea what I am talking about (and I hope you do not), try disabling your PC firewall.