Not sure if it's misconfigured, but select @@datadir; returns:
[CODE]+-----------------+
| @@datadir       |
+-----------------+
| /var/lib/mysql/ |
+-----------------+
[/CODE]

/var/lib/mysql doesn't contain any .sock file.

nano /etc/mysql/my.cnf lists:
[CODE][client]
port            = 3306
socket          = /var/run/mysqld/mysqld.sock

# Here is entries for some specific programs
# The following values assume you have at least 32M ram

# This was formally known as [safe_mysqld]. Both versions are currently parsed.
[mysqld_safe]
socket          = /var/run/mysqld/mysqld.sock
nice            = 0

[mysqld]
#
# * Basic Settings
#
user            = mysql
pid-file        = /var/run/mysqld/mysqld.pid
socket          = /var/run/mysqld/mysqld.sock
port            = 3306
basedir         = /usr
datadir         = /var/lib/mysql
tmpdir          = /tmp
lc_messages_dir = /usr/share/mysql
lc_messages     = en_US
skip-external-locking
#
# Instead of skip-networking the default is now to listen only on
# localhost which is more compatible and is not less secure.
bind-address            = 127.0.0.1
#
# * Fine Tuning
#
max_connections         = 100
connect_timeout         = 5
wait_timeout            = 600
max_allowed_packet      = 16M
thread_cache_size       = 128
sort_buffer_size        = 4M
bulk_insert_buffer_size = 16M
tmp_table_size          = 32M
max_heap_table_size     = 32M
[/CODE]

/var/run/mysqld/mysqld.sock and /var/run/mysqld/mysqld.pid both are 0777