For the first week a night guard brings extra saliva, a feeling of pressure on the teeth and a few restless nights. That is normal and it fades. Pain in one spot, a jaw that aches every morning or teeth that feel moved are not normal, and that is when you see a dentist.
Most of the bad side effects come from guards that do not fit, boil and bite trays from the drugstore and guards worn long after they wore out. A guard molded to your own teeth avoids most of the list.
