It appears that when a server is running DSO as the PHP handler and if a WordPress 3.5 update is needed, the maintenance file is written with ownership as user.user during the upgrade process. This may prevent the file from being removed correctly once the upgrade had completed.
The page will display:
Briefly unavailable for scheduled maintenance. Check back in a minute.
In order to repair this, log on to the server, and go to the DocumentRoot:
mv .maintenance file .maintenance.save
Clear your browsers cache and the site should then load correctly. After, there is a theme update for Twenty Twelve. Go ahead and run that.