The same error message has also been noticed with a problem with Airport firmware in the past, so that might be the issue. https://discussions.apple.com/thread/1487422?start=0&tstart=0
Is your computer an Early/Middle 2011 or newer?
If it is not then Airplay Mirroring will not be available out of the box, this is because older models cannot output enough graphics to be implemented. With a little googling its possible to change this although it is not recommended due to a poor graphical experience.
On the iOS side of thing the exact same thing is implemented with:
EOL iPhones -> iPhone 4S
EOL iPad 1 -> iPad 2 & 3
I have the same problem. Error -6722. When I went to firewall options I figured out that it was TURNED OFF.
And even in this case I was facing the error -6722.
I'm trying to mirror my display using Apple TV (3rd G) and MB Air (2012 version) on Mountain Lion Air Play. So the devices are not the problem too.
The fact is that when I do mirroring with my Bluetooth turned OFF, it all works very nice.
When I turn it on, seconds after, the error occurs. So, it seems to me that bluetooth is causing it.
But, "why should I mirror it on my TV if a can't use my keyboard and magic mouse"?
My two questions are. 1. How can I fix it? 2. Does someone know if I can have my Mountain Lion payment back (because I bought it just to mirror and use the TV as display) ?
If someone is able to help me I would be very grateful.
I'm having this same problem and nothing is fixing it. Firewall is off. I restarted my Apple TV but it gives me the same error message or error message 60 saying my device is off and i need to check and make sure it's plugged in. It is picking it up though so I know it's connect.
Also, what do you mean you can't use your keyboard and mouse with Lion? It doesn't show exactly what is on your computer screen??