I get the bad taste too... worse the next morning! Sometimes when I cough, I can taste iodine... but only when I'm going through a detox. I don't get the regular detox either... mine comes in the form of a chest cold and then disappears for a while.
For whatever reason, our lungs are our chosen detox route. Some people might say that it's because the first choice elimination organs like the colon and kidneys are blocked.. but that can't be right. Mine are squeaky clean. Be glad though... I am.
At least it's not the skin and it's bearable!