Are iodine supplements safe?

Only in safe amounts: Iodine deficiency is uncommon in the US because it is abundant in seafood, added to many other foods, and found in multivitamins. Taking more than the generally recommended daily limit of ~1000 mcg daily will increase the risk of thyroid dysfunction. Hypothyroidism occurs when excessive iodine blocks thyroid hormone synthesis. Hyperthyroidism can also occur in people susceptible to overfunction.

Yes: In fact, iodine deficiency is not unusual because there used to be high levels in dairy (it was used to clean the cow's udder, now chemicals are used.) there used to be a lot in bread because it was used as a dough conditioner (bromides are now used.) a recent study in boston showed that about 50% of pregnant women were iodine deficient. It's safe to take up to 1000 mcg daily.