How come our thyroid glands don't suffer awful mutations (or do they)?
Radioactive does not mean much in and of itself, your bones are radioactive (potassium), just being radioactive is not enough to do any damage.  It needs to be the right type of radiation and have high enough intensity before it can start damaging DNA and thus cause cancer. Second the amount of iodine in the body is miniscule, the aforementioned radioactive potassium in your body is orders of magnitude larger (if there is any radioactive iodine present at all which is unlikely). 

On top of this remember we are surrounded by low dose radiation all the time so our bodies have evolved ways to handle minor damage.http://imgs.xkcd.com/blag/radiation.png