It is confirmed since a while that the MySQL server that was distributed with CentOS 6.4 and on, for now, has a so called stale socket bug.

This happens when there is an unclean/forced shutdown or restart of the box (usually due to a power failure). The mysqld daemon is being “killed” leavinf the socket in  /var/lib/mysql/mysql.sock

so when you try to (re)start the MySQL daemon it complains with the error described as

another MySQL daemon already running with the same unix socket

This bug has been corrected but until it is updated in the repo, the only (and effective) workaround is to start the myqld daemon from rc.local:

chkconfig mysqld off

vi /etc/rc.d/rc.local

and paste at the end of the file:

rm /var/lib/mysql/mysql.sock
service mysqld start

This will remove the myql.sock file before starting the MySQL daemon for whatever reason it’s there after the mysql deamon was stooped, otherwise it will produce an (insignifficant) error during startup – with a complaint that the given mysql.sock file does’t exist.

Still, until the bug is present you don’t have to worry about this issue anymore.