I had configured a second server and everything worked fine until I upgraded to Ubuntu 12.04. Something changed in AppArmor that was blocking the socked creation. From the MySQL log file:
[ERROR] Can’t start server : Bind on unix socket: Permission denied
[ERROR] Do you already have another mysqld server running on socket: /var/run/mysqld/mysqld2.sock ?
The culprit was a change in the AppArmor configuration file. Instead of writing the full path, now you’re supposed to not write /var (????). Confusingly, the path to the original MySQL socket does have the /var!!!
To add a second server, or alter the socket and data directories, add the following lines to your /etc/apparmor.d/local/usr.sbin.mysqld :