EEEEK!! Luckily, I have no children with this issue and God help me if I did because it's my ULTIMATE pet peeve. My daughter chews gum from time to time and if I hear her chew with her mouth open even for a brief second I shoot her a look and she knows to chew with her mouth closed. I think it becomes a habit and I don't think it helps when the parents do it at the dinner table or when it doesn't bother them.

I would have a conversation about manners at the table or manners when eating. That it's not polite to show your food being chewed and when you chew with your mouth open everyone can see your chewed up food. For me, I would correct it just like you correct other behaviours like taking toys or pushing. Maybe turn his chair around when he does it until he realizes it's not going to be accepted.

Usually if it is a medical issue, you will hear a lot of breathing while eating almost like when we have a stuffy nose and can't taste our food then children are more likely to eat with their mouth open.