I've only noticed this happening if I was on a call, opened some app during the call, and continued the call while the app was still open. As long as I amon the phone screen, it always blacks out like it's suppose to, unless I have the speaker phone activated.
My note 3 screen stays on during calls also.
It stays on unless I push the lock button on the side. I don't have any apps running at the time of the phone call either. If I restart the phone it works as it should. After a few days it'll start messing up again.