by naming the checkbox with a "" you are already creating an array.
in the cc and bcc sections, use the following code to convert the array to a comma separated list:
<?php echo((isset($_POST["recipients"]))?implode(", ", $_POST["recipients"]):"") ?>
if you can see all of the addresses in the to section, as a coma separated list, but it is not sending to all of them, that is an issue with the smtp server, not the code.
if the email is going to some addresses, but not others, the smtp serter is refusing to relay the email to those address, you will need to contact the host to have them look into the smtp servers error log to see why the email is not going to those addresses.