many people will have sensitivity and some will have gum irritation from whitening, but it goes away a few days later (no known permanent side effects) and you can usually control them by experimenting with lower concentrations of peroxide, shorter wearing time and more time in between whitening sessions. usually a mild painkiller like asprin can also help control sensitivity after whitening, and if you get custom trays, your dentist can also give you a flouride or other desensitizing gel to wear in your tray after bleaching. as far as gum irritation having the custom trays made decreases peroxide leaking into the mouth so it would decrease soft tissue irritation (I find whitestrips are also very good).
