I obviously agree with Trapper because I take more than 1 gram SSKI daily often and have only good results.
But you have to realize that Iodine makes everything work faster. This means that all nutrients are used up faster. If these nutrients are not there you get a fierce reaction to the iodine. What reaction exactly depends on the nutrient that's depleted first. So look at the diet and see if it is nutrient dense. I would add those that Trapper mentioned: C, B's, selenium etc. You could advise a good multi and add extra companion nutrients + C and B's.
If a person is hypothyroid or hyperthyroid the reaction to the Iodine can be severe because either condition means that there is a severe nutrient deficiency going on. So if a person is already showing lots of signs of nutrient deficiency (like obesity) I would start low with the Iodine and start immediately with all the other nutrients. Especially take a good look at the diet.