a multiple select list will store the selections in an array. you need to use the implode function to convert the array into a comma seperated list.
change:
<?php echo((isset($_POST["Appointment_Request_group_Best_Approximate_Time[]"]))?$_POST["Appointment_Request_group_Best_Approximate_Time[]"]:"") ?>
to:
<?php echo((isset($_POST["Appointment_Request_group_Best_Approximate_Time"]))?implode(", ",$_POST["Appointment_Request_group_Best_Approximate_Time"]):"") ?>