I use Slack 8.0 and have begun to experiment with
MySQL. After I finally figured out how to install and start
the server, create some tables and access data, I
decided that I should probably start the server when
Linux starts.

I have added the following to rc.local:

echo "Start the MySQL Daemon"
/usr/bin/safe_mysqld &

which seems to work just fine.

However, I have now waded a little further into the
documentation and discover that for startup purposes,
the script "mysql.server" is recommended.

Aside from invoking input from my.cnf, if you have one,
is there any other advantage/necessity to running
this script at startup as opposed to what I have been
using?

well the mysql.server script checks for mysql processes already running and other such essential stuff - I would only consider putting the mysql.server script in - ditch your first option