I see one thing that stands out. It's the $phone variable.
Here is the syntax (from php.net) for the mail function
bool mail ( string $to, string $subject, string $message [,
string $additional_headers [, string $additional_parameters]] )
According to your php file, the following information is
being sent.....
$to is right
$subject is right
$message is right
$phone is wrong (this should be sent inside the body of your
message if you want their phone number)... according to the mail
functions parameters, this would be header information and since
this is going to be ###-###-#### and not of the form MIME blah blah
blah, the server receiving the e-mail is going to reject it. change
your mail line to this....
mail($to, $subject, $message, $headers)
also change the variable call to message to this....
$message = $_POST['visitor_comments']."
".$_POST['visitor_phone'];
and get rid of the $phone = $_POST['visitor_phone']; line as
it won't be necessary.