when using multi check boxes, or multi select lists, you need top edit the code to use the implode function to convert the array to a comma seperated list.
For example, change:
<?php echo ((isset($_POST["Appointment_request_group_Best_times[]"]))?$_POST["Appointment_request_group_Best_times[]"]:"")?>
to:
<?php echo ((isset($_POST["Appointment_request_group_Best_times"]))?implode(", ", $_POST["Appointment_request_group_Best_times"]):"")?>