mysql error log issue
You may have placed the log-error option under the wrong header.

Put it here:

[mysqld_safe]
log-error=/var/log/mysql/err.log 


Then, service mysql restart

I put it there because the mysql service in /etc/init.d calls mysqld_safe to call mysqld. In addition, /etc/init.d/mysql can pass paramaters to mysqld_safe as shown above.

Just to be safe, run this also

mkdir /var/log/mysql
chown -R mysql:mysql /var/log/mysql


Give it a Try !!!