I recently got a new job, and realize that I'm way to ignorant on mail troubleshooting. How do you recommend learning how to read email headers, mail logs, and troubleshoot various mail problems? any good books? tutorials? anything else? is the documentation comprehensive enough to start there?
The extensive Exim documentation and the book by the Exim author are good places to start, to get an idea of how to make things work and consequently what can go wrong. Whilst they focus on exim configuration and use, they also discuss more general email topics. You should then consider setting up some different mail servers for some essential hands-on experience, and to understand how they work with other systems like DNS.
I'm going to be somewhat facetious here and recommend RFC 2821. That's as good a place to start as any.