Great to hear that it works. Just upgraded, and sure enough problem solved.
Here is some more detail for folks who are coming into this thread later.
References:
Prefs = Dock - Systems preferences - sharing - Remote Management - Comnputer Settings button
Checkbox = "VNC viewers may control screen with password"
If you are running Apple remote Access 3.8.5, Apple yet again broke the program. Previous to 3.8.5 you could select the checkbox in prefs and use a VNC viewer to see your desktop remotely. Now you get an error.
One solution that worked was to use VNC viewer (5.3.1 r17370) Connecting via apple screen sharing rather than "VNC viewer mode". Having the checkbox cleared was the solution. Counter intuitive. You would then get a VNC (tested on windows 8.1) window asking for user/pass for remote system and gain access to the computer. TightVNC would fail, as it was trying to use the checkbox method of authentication and that had to be off to work so normal VNC viewers were broken.
With release 3.8.5.1 This is fixed - TightVNC with the checkbox selected will show you a window to put in your vnc password, then you get a traditional login screen view from your remote mac. Yes VNC viewer also works, and still also works in the other method mentioned above of checkbox being cleared.
Till Apple breaks ARD next time....