这不是什么好事，我也脸上无光。

But it's not the worst thing that could have happened.

儿子被老板解雇，他父母都为他感到脸上无光。

The parents felt ashamed for their son when he was dismissed by the boss.

因为丢了表格是一种失职的表现，这事要是让外人知道了会让自居办事严谨的领导们脸上无光。

Because losing a form is a type of incompetence, the exposure of which would cause the authorities to lose face by contradicting their implicit claim to be people who can properly handle forms.