I have the same problems..when i try to log in i keep getting the red message "Could not sign in, please check your network connection" etc etc
I have tried changing the DNS to 8.8.8 etc..etc..did not work..
My face time preferences are greyed out (meaning I cant access the option)
I have deleted related .plist files
I have tried using different apple ID's..my wifi connection is fine...
I have a serial number
I have checked my date & time preferences..interesting thing doing that is keeps saying "unable to determine current location at this time" even when i select the correct time zone locations (maybe that is the problem?)
I am connected via wifi to our house network..
I have tried the several solutions as listied on the forums..they havent worked..
I guess a reinstall of mountain lion is the option or deleting the facetime application and reinstalling it separtely..
but then how does that work as i see it costs .99 cents to purchse when i already have it as part of Mountain Lion..
Shrugs..I have called apple support and they have been reasonable..its just, it seems that this is a problem that is effecting others and it does need a better repair option..it's a flagship application and it should work properly..this is one problem that is driving me much annoyed!..
Thanks..NMBY