As for this poster's statement: Would supplementing iodine be good for someone with hyperthyroidism? No.
It is absolutely unfounded and ridiculous.
Not if you really understand chemistry and how the body works.
Hypo, as well as Hyperthyroidism is caused by heavy metals like Mercury and other pseudo-iodines occupying the cellular receptor sites normally utilised by iodine.
This is a great example of what I mean. Hypothyroidism has numerous causes including hypothalamus or pituitary dysfunction, excess estrogen, exposure to other halogens, poor adrenal function, chronic stress leading to elevated rT3 and poor T4 to T3 conversion, low iodine and Hashimoto's. Mercury is not a "pseudoiodine". It's structure is not even close enough to occupy iodine receptors. Also keep in mind that mercury has a high affinity for fats, which is why the brain is so affected by mercury. The thyroid is not a primary target of mercury.
As for hyperthyroidism, the most common causes of this are autoimmunity, which is not caused by heavy metals and excess iodine.
Mercury occupying the receptor sites of the bodies many organs glands and systems also greatly impairs the proper hormone regulation through the same vehicle of blocking receptor sites.
This is again a great example of why people need to do real research rather than rely on opinion sites. For example this study which shows only a slight effect on the thyroid by mercury vapors: