Try using this command to check the email in exim's log for CentOS and RedHat systems:
Code:
exigrep user@domain.com /var/log/exim_mainlog
If your machine is FreeBSD, it would be this command:
Code:
exigrep user@domain.com /var/log/exim/mainlog
You would replace user@domain.com with the email address recipient, the one that was rejected.
Next, I'd suggest trying this command for that same email address:
Code:
exim -bt user@domain.com
This will show if the email address properly routes on your machine or not (it should route locally if that email address is on the machine and properly setup.