Got error: 2002: Can't connect to local MySQL

I`m new in this forum sorry for my english. I am reciving an error in the text report that is send to my email, after a full backup of a website (CPanel). The administrator of that hosting is saing that everything is ok, but i`m not so shure about those backups. I need another comfirmation so i`ll post a part from the text . I need some help . THX

I see an arhive after backup, but if i make a backup and after a few minutes i make another the diference of mb are so large . ( 100 mb or 300 )

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Waiting for load to go down to continue
Waiting for load to go down to continue
Done
Entering timeout safety mode
Determining mysql dbs...Saving mysql privs...Done
...mysql version: 5.1......mysqldump version: 5.1......Done
Storing mysql dbs...adlssska_smcf1.........
(0 bytes) adlssska_5.........
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(0 bytes) adlssska_3(0 bytes) adlssska_1.........
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/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
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(0 bytes) adlssska_4/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) horde.turba_objects/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) horde.horde_prefs/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
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(0 bytes) horde.kronolith_events/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) horde.kronolith_storage/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) horde.mnemo_memos/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) horde.nag_tasks/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) roundcube.users,roundcube.messages,roundcube.identities,roundcube.contacts/usr/bin/mysqlcheck: Got error: 2002: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2) when trying to connect
(0 bytes) ...Done
Copying cpuser file.......Done
Copying crontab file.......Done
Copying quota info.......Done
Storing Subdomains....
Done
Storing Parked Domains....
Done
Storing Addon Domains....
Done
Storing ssl domain......Done
Copying password.......Done
Copying shell.......Done
Creating Archive ..../bin/gtar: backup-11.22.2010_09-11-36_adlssska/homedir.tar: file changed as we read it
Done
pkgacctfile is: /home/adlssska/backup-11.22.2010_09-11-36_adlssska.tar.gz
md5sum is: 3a972cfc2779f6eec9e5999bbcf32bb4

size is: 408972179
/bin/gtar: /home/backup-11.22.2010_09-11-36_adlssska/homedir.tar: Cannot open: No such file or directory
/bin/gtar: Error is not recoverable: exiting now
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