Made a quick check on the local news archives (about Chernobyl and iodine), and found a few interesting facts.

There was a radioactive iodine scare in Scandinavia back then, and lots of people took iodine tablets for 14-28 days after the accident.

According to late 80s leading local scientists that in the news reports remain anonymous however, radioactive iodine is pretty short range, primarily causing havoc and long term effects within about 100 km radius (about 60 miles), and it's not something that is easily spread by wind.

(according to the news at the time) Radioactive iodine can be absorbed by some fungi, including several edible kinds, and this somehow slows the final break down of the iodine => mushrooms can be radioactive/contain very high amounts of iodine for several months after unabsorbed fallout has dispersed.

Probably a great blow for Japanese, who (like us Scandinavians) still collect lots of wild mushrooms.

And like Philip mentions, iodine tablets aren't healthy either, and can cause rash, nausea, numb extremities and metallic taste in mouth (at least those were reported at the time, signs for seeing a doctor I suppose).

The 130mg pill is about the highest allowed level for iodine per day, and you can get even amounts up to that from seaweed, and lesser amounts from any seafood and salt with added iodine, so balance your diet if you decide to take the pill.

-jh