Bladderwrack and hypothyroid.
You'll find that hypothyroidism is very very rarely caused by too little iodine.
Bladderwrack is suggested all too often on the various herbal mailing lists. It's pulled out whenever anybody at all posts about his or her problems due to low thyroid function.
Bladderwrack (Fucus vesiculosus) is of use if the hypothyroidism is due to iodine deficiency, because it (and other seaweeds) contain lots of iodine (and of course, a host of other minerals).
If low iodine intake is not the problem, bladderwrack is a nice mineral herb which can be a problem if the low thyroid function is due to too much iodine.
Used to be, all hypothyroidism was due to lack of iodine. You'd get a nice goiter, and inland places with no access whatsoever to sea salt or salt sea fish (and seaweeds, but seaweeds weren't generally considered as food, back then) would consider goiters to be so normal that they'd decorate them. Great big chunks of finely worked precious metals, hanging over bulging throats ...
So you'll find bladderwrack (and other seaweeds) suggested as a major cure for goiter (and thus, low thyroid function), in all the old books.
... these days, if you're eating a Western diet, you get more than enough iodine in your iodized salt, in your processed foods (which contain iodized salt), and in your saltwater seafood.
Hypothyroid due to iodine deficiency is now a thing of the past, except for a few food fanatics who avoid sea salt (and iodized salt) at all cost, who don't eat any processed food (iodized salt in that) and who don't eat seafood.
The main cause for hypothyroid, now, is a lack of growth hormone because of too much insulin. Read more about that in my Syndrome X series.