Normally Exim runs very well out of package, and there is no need to do much tweaking on it. These are just some watch points that may need a little attention.
The never_users list
In /etc/exim.conf, root is in the “never_users” list. This is described as a “paranoiac” security catch. The only problem I had was that the email delivered to root from the cron job got bounced and it was flooring the exim mail log. To cure this, either you have to create an local alias for root so the emails will be forwarded to that user; or change the cron job email destination to something other than root. I chose the latter option.
Running smtp on another port
The reason for this is that some ISPs start to block post 25. So from your email client you will see some “connection timeout” error. Opening another port, and configuring your email client to connect to the new one can help bypassing this “restriction” from your ISP if it is there.
If you have Cpanel installed, start another exim on a different port is quite easy. Just go to “Service Configuration”->”Service Manager” page and setup “exim on another port”.