I just bought an Apple TV today and was experiencing similar problems with Video mirroring from my Macbook Pro 2011. I am working on a 10.9.1 operating system with 2.3 GHz Inter core i5 and 4Gb of DDR3 memory.
When I set up the Apple TV, the image would freeze on my TV as soon as I activate airplay mirroring. What ever image was on my Macbook screen would apear on my TV and that would be it. There would be no more video mirroring. I could not see the mouse move, or any video playback, or any applications...Basically I would be stuck at the image that I had when I started mirroring.
The audio playback was normal throughout however. Even when the image was frozen the audio would work just fine.
When I set up the apple TV it was connected to my network wirelessly. I connected my Apple TV to my router via ethernet cable and that solved the problem.
Now, I have excellent video playback. I have excellent audio playback. I can stream videos from the internet on my computer and watch them on the TV via apple TV. I can access my itunes from my computer and listen to songs through my TV and there is no lag or missed frames.
My router does not support a 5G signal so I could not try that option, but it seems that the ethernet cable works great.
Quite a disappointment from apple, but at least there's a fix to the problem.