I should have read this before buying and wasting time with them - see my note to apple:
After a frustrating 2 hour call on why airplay in Mountain Lion did not work properly - see transcript of case # 356682008 - i was told to connect via ethernet cable to identify the issue. Ethernet Cable - in my household they went the way of dinosaurs as the one feature that made me upgrade to mountain lion was the ability to use airplay wirelessly - without having to connect the $60 Apple cable to my HDTV anymore. I do not even know the last time I had an ethernet cabe in my hands.
The fact that nowhere in your literature as of this morning requested an ethernet cable as part of the specification for use of the features of Mountain Lion basically equates to false advertising - either that or the MacBook Pro you sold me lack some of the functions that you were supposed to provide - I would like to know how are you going to fix this situation that does not require me to waste any more of my billable time with you.
Mirroring will work if your connection from your computer to the wifi router is at a fast enough speed. For example if you use an apple airport, set your airport to connect at 5Ghz which will up your link speed. The faster your 892.11 network is then the traffic between the Apple TV -> wifi router <- computer will be and airplay will just work!