Well you probably won't see the errors from the user-side, as I assume you also have display_errors turned Off...??
For information on error logging, see this manual page: [man]ref.errorfunc[/man]. Basically, you simply point the error_log variable to a file that the webserver can write to, enable the log_errors, directive (and disable display_errors if you haven't already!), and set error_logging to a generous level (I normally leave it at E_ALL).
Other than that... it's really hard to track an e-mail's progress once the SMTP gateway accepts it. It could be silently blocked as spam without you ever knowing, who knows.