Warning: include_once(sites/all/themes/essexdfa2/template.php): failed to open stream: No such file or directory in mailsystem_theme_theme_registry_alter() (line 45 of /home/essexdfa/public_html/sites/all/modules/mailsystem/mailsystem.theme.inc).
Warning: include_once(): Failed opening 'sites/all/themes/essexdfa2/template.php' for inclusion (include_path='.:/usr/share/php:/usr/share/pear') in mailsystem_theme_theme_registry_alter() (line 45 of /home/essexdfa/public_html/sites/all/modules/mailsystem/mailsystem.theme.inc).
When the mailsystem theme is not the same as the currently active theme - for instance if 1) you have a special theme created for mail, or 2) you're on an administration page and the administration theme is different than the default theme - mailsystem attempts to load all of its theme's preprocess code, by calling include_once() for each template.php in the theme's set of base themes.
The problem is that there are some base themes (Fusion is one example, which I happened to be using) that by default do not provide any template.php for their subthemes - at least out-of-the-box the subtheme refers back to the base theme for its preprocess functions. Mailsystem assumes, however, that there is a template.php in its theme directory and calls include_once() without checking first to see if template.php exists, causing an E_Warning to be generated.
Wrap the include_once() calls for template.php - both for the mailsystem theme and each of its (possible) base themes) - with a call to file_exists() or is_readable().