Many people chew with their mouths open. It does not look too good. Besides that, is it good or bad?

As you correctly say – it does not look good. Mouth breathers are normally the one’s because they cannot breathe through their nose. Mouth breathers create other problems for themselves as well. It is certainly better to chew with your mouth closed which is easier to do if you take smaller mouthfuls. Then try to train yourself to breathe through the nose. Nose breathing also allows you to relax more. Refer to the article on “Natural Breathing” and “Nose Breathing”.