I have a similar problem. Sometimes the Airplay works fine with both video and sound. At other times, the video plays through the TV but the sound comes out of the Mac speakers. When this happens, "Apple TV" appears on the sound menu (ALT + speaker symbol on menu bar) but cannot be selected. Rebooting the Apple TV does not help and neither does logging off and on again on the Mac. However, rebooting the Mac makes it work again, although the problem typically comes back by the next day.
(iMac (mid 2011) OS X 10.8.3, Apple TV 2nd gen: software 5.2.1)
I could not change the sound from internal speakers to Apple TV either. The following work-around solution worked for me, as an alternative to rebooting the computer. In a terminal window, type:
sudo killall coreaudiod
I hope this works for you. You can find more on this in the following discussion: