When I run exim -d test@domain it delivers fine, but when I send a message from the mail command, I get User unknown and the mail is saved in dead.letter.

It looks as if Exim isn't being called by mail; instead it is calling some other program (probably Sendmail). Try running the command

/usr/sbin/sendmail -bV

(If you get No such file or directory or Command not found you are running Solaris or IRIX. Try again with /usr/lib/sendmail.) The output should be something like this:

Exim version 4.05 #1 built 13-Jun-2002 10:27:15
Copyright (c) University of Cambridge 2002

If you don't see this, your Exim installation isn't fully operational. If you are running FreeBSD, see `FAQ/FreeBSD/Q9201`_. For other systems, see `FAQ/Building_and_Installing/Q0114`_.