Notice: Undefined index: to in DefaultMailSystem->mail() (line 83 of /var/www/example.com/public_html/modules/system/system.mail.inc).

Notice: Undefined index: to in DefaultMailSystem->mail() (line 83 of /var/www/example.com/public_html/modules/system/system.mail.inc).

You forgot the $message['to'] part of $message.

You could be using a main function direct, mail($message);, or the following drupal_mail function with an invalid $to. An invalid $to is unlikely because processing will almost always stop with an earlier error message.
drupal_mail($module, $key, $to, $language, $params, $from, $send)

The following function could be missing the to address and could remove the default built by Drupal.
hook_mail($key, &$message, $params)

If your module is named example, the module would contain the following function. The function can remove anything from $message including $message['to'].
function example_mail($key, &$message, $params) { }