Okay, Michael, I tok you suggestion and Googled the above. The very first result was in regards to my host, Yahoo Small Business.
According to Yahoo's help page:
"When you send email with a Perl or PHP script, you will need to make sure that the "From:" address in your email header is set to an address within your domain name. If the address is set to an external email address, then you will see an error in your /tmp/mailError.log file. For example:
2003 Jun 18 21:18:15 Result: 9
2003 Jun 18 21:18:15 From address not in member domain. Message not sent.
With the Perl/PHP mail feature, you will be limited to 250 emails per day. This means that once you have reached this limit, the email generated by your scripts will not be sent until this limit has been reset.
Please note that these emails will not be held for delivery, so you may later need to regenerate the emails if your script has reached the 250/day email limit."
I have followed Yahoo's instructions for "automatically" setting the "From" in my mail script, (filling out a form on my server) but that hasn't worked. I have also found some threads in this forum that reference the same error, but in regards to posting via e-mail, which would equal sending email via PHP, not receiveing it.
When I'm logged in and post a comment, the notification shows it as having come from my e-mail address, not from WordPress or whatever. I'm assuming the same thing happens when other user post comments, since I have "Comment author must fill out name and e-mail" selected in Discussion Options.
This would mean that the "From" field in any comment notification would always be from an e-mail address that is NOT on my domain, unless I am posting a comment as administrator (which explains why I'm only getting notified for my own comments). If I turn off that option and post a "test" comment as an anonymous user, it is e-mailed to me immediately.
In the threads regarding posting via email, some people have found that their scripts allow you to specify either the TO or FROM field, but according to Yahoo you must specify the FROM field. Changing this Yahoo's way didn't work, so now I'm wondering if I can change it manually in one of the WP files. But I'm not sure which file in 1.5.2 contains this function. I've found this info for 1.5 and 1.5.1, but when I check those files on my latest install, I don't find the same code the previous threads reference.