This is a very specific case, but:

- postfix is configured to have a special port dedicated to mailman, which
  bypasses normal delivery restrictions

- the normal smtp port works fine for delivery

- the mailman port doesn't, and complains of errors like:

postfix/smtpd[]: NOQUEUE: reject: RCPT from unknown[127.0.0.1]: 451 4.3.0 <user@example.com>: Temporary lookup failure; from=<list@example.com> to ...

There are a lot of these, because a mailing list post goes to lots of
addresses, which can hide the fact that this line might also be present
somewhere:

postfix/smtpd[]: warning: connect to mysql server unix:/var/run/mysqld/mysqld.sock: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

...This line is caused by postfix being set to chroot (which it does by default
in master.cf, unless you tell it not to, and which it can do per service in
master.cf -- e.g. normal smtp can be not-chrooted [which explains why it
works], but you left the special port with default settings), so
/var/run/mysqld doesn't exist in the chrooted environment. The solutions are:

- Don't chroot

or

- Connect to mysql with TCP/IP instead of socket