For a few weeks now, I've been seeing this error in my logs every night:

/etc/cron.daily/logrotate:
error: error running shared postrotate script for /var/log/mysql.log /var/log/mysql/mysql.log /var/log/mysql/mysql-slow.log
run-parts: /etc/cron.daily/logrotate exited with return code 1

What's happening is that after all the mysql backing up and everything is done, ubuntu is trying to use the debian-sys-maint user to flush the logs, this is actually called in /etc/logrotate.d/mysql-server. On my system, we seem to have lost this mysql user.

The solution is to look for the password used in the /etc/mysql/debian.cnf file, mine looks like this:

# Automatically generated for Debian scripts. DO NOT TOUCH!
[client]
host     = localhost
user     = debian-sys-maint
password = xxxxxxxxxxxxxxxx
socket   = /var/run/mysqld/mysqld.sock
[mysql_upgrade]
user     = debian-sys-maint
password = xxxxxxxxxxxxxxxx
socket   = /var/run/mysqld/mysqld.sock
basedir  = /usr

Using the password, and some inspiration from this post on the Ubuntu Forums I recreated the user with the necessary permissions and password with:

GRANT RELOAD, SHUTDOWN, PROCESS, SHOW DATABASES, SUPER, LOCK TABLES ON *.* TO 'debian-sys-maint'@'localhost' IDENTIFIED BY PASSWORD 'xxxxxxxxxxxxxxxx'

This did the trick, as the nightly errors have now disappeared from my script. Hope this helps someone in a similar situation - if you can expand these notes then please add a comment and I will update this as needed - thanks :)