I'm seeing similar reports to this, but nothing that fits exactly.
I have a Airport setup with an extreme and two expresses. One express only does Airtunes (it is an older model at 6.3) and is hooked up to the stereo. I can talk to it via ethernet. The other express extends the wireless from the extreme. Both are at 7.6.1.
I run iTunes mostly on a Mac Pro. Because Apple system descriptions are stupid, I have no idea what "year" it is. I bought it a few years ago. I don't care about Airplay Mirroring. I have an Apple TV on the network, but that doesn't enter into this discussion.
Prior to Mountain Lion I would choose one or more speakers to output music to. Usually, I select "Living Room" and the 6.3 express will stream to the stereo input.
Now with Mountain Lion I cannot select any remote speakers. It spins on 'Connecting to "Living Room"...' for a long time and then just dismisses this dialogue. No error message is ever given. Nothing in the console log other than "Stopping AirPlay". Same thing for any other AirPlay device in the iTunes speaker drop-down.
During my troubleshooting, I ended up in the Sound Preferences, and could see "Living Room" in the Output panel. If I selected that, iTunes would select the same output in its "speakers" thingy. No other AirTunes/AirPlay devices were there. I changed all airport devices so that they used "auto" (and "host", if that was available) IPv6 and now all three AirPlay devices show up in the Sound Prefs, but I can no longer select them. The Mac is already using auto IPv6.
So, I guess if I switch everything back to IPv6 local I might be able to choose one of the devices as the default output device, but this is pretty much an egregious hack.
This might seem minor, but this is the first time I've considered rolling back to a previous release.