I no longer think that this error is related to my problem. It has to do only with one of the add-ons, which I am not using right now.
The errors that I posted above are output after the mail is logged. Here are some errors that it puts out before logging the mail:
2012-10-18 10:54:25 000000 -- PHP [E_NOTICE] 8 : Trying to get property of non-object in /home/efield5/public_html/wp-includes/post-template.php at line 30
2012-10-18 10:54:25 000000 -- PHP [E_STRICT] 2048 : Non-static method nggGallery::get_option() should not be called statically, assuming $this from incompatible context in /home/efield5/public_html/wp-content/plugins/nextgen-gallery/lib/shortcodes.php at line 47
2012-10-18 10:54:25 000000 -- PHP [E_STRICT] 2048 : call_user_func_array() expects parameter 1 to be a valid callback, non-static method GA_Filter::the_content() should not be called statically in /home/efield5/public_html/wp-includes/plugin.php at line 170
2012-10-18 10:54:25 000000 -- PHP [E_STRICT] 2048 : Non-static method GA_Filter::ga_parse_article_link() should not be called statically in /home/efield5/public_html/wp-content/plugins/google-analytics-for-wordpress/googleanalytics.php at line 1282
I don't have the time or know-how to track down these errors. :(
Also, I said above that the email preview worked fine. Well, that's only partly true. The email preview shows the theme and email title, but it doesn't show any of the actual email text. The same is true if you try to view the email in your browser from the link -- there isn't any of you message there, just the theme with the email title.
I am still trying to figure this out, but I don't know enough about how the plugin works to know what might be causing this.