I'm not specifically concerned with dental health, as that's reliant upon diet more than anything else, but without chewing certain plants everyday, wouldn't everyone have had awful breath? Was the chewing of things like spearmint common? Was bad breath something so common that no one noticed that it was bad?
It certainly was noticed at least in some times in some places in the past.
The Talmud talks about it in relation to priests and spouses, in Ketubot 72b and 77a. It's considered one of the serious disabilities that are grounds for a husband to divorce his wife if it isn't noticed until after the wedding.
Hippocrates gave advice for bad breath – regularly rinsing the mouth with wine, dill, and anise.
The Ebers Papyrus from Egypt in the 16th century BCE gives a recipe for toothpaste – mint, pepper, salt, and iris.
The Romans also used a toothpaste, with pumice, baking soda, and sodium bicarbonate.
So while depending on where and when you're talking about, you certainly could have found a relatively high level of oral hygiene, and certainly a concern with malodorous breath.