mysqldump error: Got packet bigger than max_allowed_packet'

1. You can add --max_allowed_packet=512M to your mysqldump command.
2. Or add max_allowed_packet=512M to [mysqldump] section of your my.cnf (thanks @Varun)

Note: it will not work if it is not under the [mysqldump] section...

Some of my scripts stopped working after an upgrade to Debian 9 & MariaDB.

MariaDB on Debian introduces a new config file specifically for mysqldump settings (/etc/mysql/conf.d/mysqldump.cnf). If you had set a max_allowed_packet <> 16M in your standard /etc/mysql/my.cnf previously, the new config file will overwrite that setting. So be sure to check this new config file and either delete the entry or adjust it to your needs.

I'm not sure if the change was introduced by the swap from MySQL to MariaDB or if Debian made a change in how the config files are laid out in V9.