I host a site for a person that does everything via blackberry and wants to email posts to the site. She has sent one post to the designated mailbox, but 24 hours later the post is still not showing. Where do I start checking what is going wrong in the process?
You're obviously posting it to a mailbox that WordPress is accessing, so check the mailbox that your friend has sent an email to, if the email is still in there then WP hasn't taken it out and thus your email settings in WP are probably wrong. If the email isn't in there your friend has probably sent it to the wrong address, not sent it at all or WP may not have read it correctly.
This is just the first step into determining the problem, tell us how you get on.
According to this article, you need to add an i-frame to your footer.php file that will call wp-mail.php whenever your site is loaded. Apparently this file will process your inbox and create the posts. This isn't mentioned in the documentation. I've tried the setup, the mail got removed from the inbox, and the post got created, in a pending state. Not quite what the config page says...
There is a great service called posterous - http://posterous.com/ - that makes this very easy, and your client will appreciate (it also does facebook, tweets, etc)
to post to WP by email uses xml-rpc - I have run into situations where certain hosts restrict this file in the security configuration, I would start there.