I see the problem.... the issue is that even if you leave both blank you are inserting the space between the date and time.
You have bound the value to:
<?php echo((isset($_POST["slide_start_date"])." ".($_POST["slide_start_time"]))?$_POST["slide_start_date"]." ".$_POST["slide_start_time"]:""); ?>
Instead try using:
<?php echo((isset($_POST["slide_start_date"])?$_POST["slide_start_date"]:"") . (isset($_POST["slide_start_time"])?" ".$_POST["slide_start_time"]:"")); ?>