I just upgraded two machines to Mountain Lion. The first being a Mac Mini mid 2011 with no problems. The second being an aluminium Macbook. The Macbook audio was dead once installed, all I got was a cross out audio option when trying to increase or decrease the volume. In System Preferences the only thing that showed was headphones and even they didn't work.

I am sure Apple are working on the fix but for now you can do this:

• Open Activity Monitor found in Applications -> Utilities folder.
• Click on the CPU button at the bottom of the Activity Monitor window. The one to the left of System Memory.
• At the top change the drop down that says 'My Processes' to 'All Processes'
• In the search box next to that type this in, or part of it at least. Even typing 'core' will find it.
• Search for coreaudiod
• Select it and then click 'Quit Process'

You might find it doesn't quit. I clicked quit and force quit. Either way once you have done this you should find your audio is back.