Not really, but... Chewing sugarless gum, especially gum with the artificial sweetener Xylitol, can actually reduce the start of new cavities. Gum made with sugar, however, does the opposite. Note also that chewing stimulates the "Vago-Vagal Reflex," which encourages your GI Tract to produce acids and excess digestive enzymes. If you have an acid reflux problem or an ulcer, speak to your MD/DO before chewing gum.
Not if sugarless. Usually not. Actually, chewing sugarless gum (those sweetened with xylitol are best) can actually protect the teeth from dental decay.