Usually none. Usually, removing a single parathyroid gland/tumor is straightforward and complications are rare. It is common, however to have a deficiency of vitamin d while hyperparathyroid, and this will need to be corrected after the surgery. Infrequent complications could include hoarseness, permanent low calcium and parathyroid levels, or hypothyroidism, in the rare case where the thyroid is taken out.
Normal blood calcium. The reason for surgery is to restore blood calcium to normal. It may go down to below normal range for a while resulting in tingling feelings in the arms legs and face or even hand cramping but that should go away with time.