Attempted to change database drive resulted in "Can't connect to local MySQL server through socket"

I attempted to move my database to a different mount on my Ubuntu installation on an amazon EC2 instance, because it was filling up the root directory. I think I've borked something up. When I run:

$ sudo mysqld --datadir=/var/lib/mysql --user mysql
110412 11:36:44 [Warning] Can't create test file /mnt/var/lib/mysql/ip-10-244-207-161.lower-test
110412 11:36:44 [Warning] Can't create test file /mnt/var/lib/mysql/ip-10-244-207-161.lower-test

In /var/log/mysql/error.log:

110412 16:01:27 [Note] Plugin 'FEDERATED' is disabled.
/usr/sbin/mysqld: Can't find file: './mysql/plugin.frm' (errno: 13)
110412 16:01:27 [ERROR] Can't open the mysql.plugin table. Please run mysql_upgrade to create it.
/usr/sbin/mysqld: Can't create/write to file '/mnt/tmp/ibRTnZix' (Errcode: 13)
110412 16:01:27  InnoDB: Error: unable to create temporary file; errno: 13
110412 16:01:27 [ERROR] Plugin 'InnoDB' init function returned error.
110412 16:01:27 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed.
110412 16:01:27 [ERROR] /usr/sbin/mysqld: Can't create/write to file '/mnt/var/lib/mysql/ip-10-244-207-161.pid' (Errcode: 13)
110412 16:01:27 [ERROR] Can't start server: can't create PID file: Permission denied

The file ip-10-244-207-161.lower-test does not already exist:

ls -l /mnt/var/lib/mysql
total 20532
-rwxr-xr-x 1 mysql root         0 2011-02-28 22:23 debian-5.1.flag
-rwxr-xr-x 1 mysql mysql 10485760 2011-04-12 07:31 ibdata1
-rwxr-xr-x 1 mysql mysql  5242880 2011-04-12 07:31 ib_logfile0
-rwxr-xr-x 1 mysql mysql  5242880 2011-02-28 22:23 ib_logfile1
drwxr-xr-x 2 mysql root      4096 2011-02-28 22:23 mysql
-rwxr-xr-x 1 mysql root         6 2011-02-28 22:23 mysql_upgrade_info
drwxr-xr-x 2 mysql mysql     4096 2011-04-11 08:22 scrapy_cache

The directories seem to be accessable:

$ ls -l /mnt/var/lib/ | grep mysql
drwxr-xr-x 4 mysql mysql 4096 2011-04-12 07:31 mysql

$ ls -l /var/lib/ | grep mysql
lrwxrwxrwx 1 mysql     root      18 2011-04-12 09:05 mysql -> /mnt/var/lib/mysql

ls -ld /mnt/{,var/{,lib/{,mysql}}}
drwxr-xr-x 5 root  root   4096 2011-04-12 07:27 /mnt/
drwxr-xr-x 3 mysql root   4096 2011-04-12 07:29 /mnt/var/
drwxr-xr-x 3 mysql ubuntu 4096 2011-04-12 07:33 /mnt/var/lib/
drwxr-xr-x 4 mysql mysql  4096 2011-04-12 07:31 /mnt/var/lib/mysql

The parts I changed in my.cnf:

user            = mysql
socket          = /var/run/mysqld/mysqld.sock
port            = 3306
basedir         = /usr
datadir         = /mnt/var/lib/mysql
tmpdir          = /mnt/tmp
skip-external-locking

I would really appreciate some help on this as I've failed miserable while trying to debug it.

I did a sudo chown -R mysql /mnt/var/lib/mysql so everything should be owned by the mysql server. /mnt is most certainly writable as I ran mv /var/lib/mysql /mnt/var/lib/ when I migrated. Mount confirms this:

$ mount | grep /mnt
/dev/sda2 on /mnt type ext3 (rw)

The disk is not full in space and it hasn't run out of inodes, disk quota don't seem to be active I installed repquota but it outputted absolutely nothing:

$ df -h /dev/sda2
Filesystem            Size  Used Avail Use% Mounted on
/dev/sda2             335G  2.0G  316G   1% /mnt

$ df -i /dev/sda2
Filesystem            Inodes   IUsed   IFree IUse% Mounted on
/dev/sda2            44564480     104 44564376    1% /mnt

Creating things as the MySQL user works, as suggested in the comments:

$ su -s /bin/bash - mysql

$ touch /mnt/var/lib/mysql/ip-10-244-207-161.lower-test

$ ls -ld /mnt/var/lib/mysql/ip-10-244-207-161.lower-test
-rw-r--r-- 1 mysql mysql 0 2011-04-12 14:10 /mnt/var/lib/mysql/ip-10-244-207-161.lower-test

$ rm -f /mnt/var/lib/mysql/ip-10-244-207-161.lower-test
$ ls -ld /mnt/var/lib/mysql/ip-10-244-207-161.lower-test
ls: cannot access /mnt/var/lib/mysql/ip-10-244-207-161.lower-test: No such file or directory

MySql isn't running.

$ ps aux | grep mysql
ubuntu   20825  0.0  0.0   3700   776 pts/1    S+   15:40   0:00 grep --color=auto mysql

/etc/mysql/my.cnf

#
# The MySQL database server configuration file.
#
# You can copy this to one of:
# - "/etc/mysql/my.cnf" to set global options,
# - "~/.my.cnf" to set user-specific options.
# 
# One can use all long options that the program supports.
# Run program with --help to get a list of available options and with
# --print-defaults to see which it would actually understand and use.
#
# For explanations see
# http://dev.mysql.com/doc/mysql/en/server-system-variables.html

# This will be passed to all mysql clients
# It has been reported that passwords should be enclosed with ticks/quotes
# escpecially if they contain "#" chars...
# Remember to edit /etc/mysql/debian.cnf when changing the socket location.
[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
#

#
# * IMPORTANT
#   If you make changes to these settings and your system uses apparmor, you may
#   also need to also adjust /etc/apparmor.d/usr.sbin.mysqld.
#

user        = mysql
socket      = /var/run/mysqld/mysqld.sock
port        = 3306
basedir     = /usr
datadir     = /mnt/var/lib/mysql
tmpdir      = /mnt/tmp
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
#
key_buffer      = 16M
max_allowed_packet  = 16M
thread_stack        = 192K
thread_cache_size       = 8
# This replaces the startup script and checks MyISAM tables if needed
# the first time they are touched
myisam-recover         = BACKUP
#max_connections        = 100
#table_cache            = 64
#thread_concurrency     = 10
#
# * Query Cache Configuration
#
query_cache_limit   = 1M
query_cache_size        = 16M
#
# * Logging and Replication
#
# Both location gets rotated by the cronjob.
# Be aware that this log type is a performance killer.
# As of 5.1 you can enable the log at runtime!
#general_log_file        = /var/log/mysql/mysql.log
#general_log             = 1

log_error                = /var/log/mysql/error.log

# Here you can see queries with especially long duration
#log_slow_queries   = /var/log/mysql/mysql-slow.log
#long_query_time = 2
#log-queries-not-using-indexes
#
# The following can be used as easy to replay backup logs or for replication.
# note: if you are setting up a replication slave, see README.Debian about
#       other settings you may need to change.
#server-id      = 1
#log_bin            = /var/log/mysql/mysql-bin.log
expire_logs_days    = 10
max_binlog_size         = 100M
#binlog_do_db       = include_database_name
#binlog_ignore_db   = include_database_name
#
# * InnoDB
#
# InnoDB is enabled by default with a 10MB datafile in /var/lib/mysql/.
# Read the manual for more InnoDB related options. There are many!
#
# * Security Features
#
# Read the manual, too, if you want chroot!
# chroot = /var/lib/mysql/
#
# For generating SSL certificates I recommend the OpenSSL GUI "tinyca".
#
# ssl-ca=/etc/mysql/cacert.pem
# ssl-cert=/etc/mysql/server-cert.pem
# ssl-key=/etc/mysql/server-key.pem



[mysqldump]
quick
quote-names
max_allowed_packet  = 16M

[mysql]
#no-auto-rehash # faster start of mysql but no tab completition

[isamchk]
key_buffer      = 16M

#
# * IMPORTANT: Additional settings that can override those from this file!
#   The files must end with '.cnf', otherwise they'll be ignored.
#
!includedir /etc/mysql/conf.d/