Can a surgeon accidentally removing a 1.5 cm mass of extra thyroid tissue or parathyroid gland cause significant hormone/thyroid problems in future?

Possibly. Damage or excess removal of those tissues may result in underactive thyroid. There are 4 parathyroid glands so damage to one or two should not cause hypoparathyroidism. Either way such a patient should be followed with periodic testing of thyroid function and parathyroid functions such as serum calcium levels by the endocrinologist or head and neck surgeon.