There are two primary concerns with consumption of excess iodine:
Now those taking extra iodine or painting the scrotum with iodine would argue that they are not taking enough to trigger iodine-thyroid issues. This idea would would seem debatable, because the RDA for iodine (in an adult male) is actually a very small number: 150 mcg/day. Those using iodine are definitely megadosing. And, what they seem to be ignoring, is the fact that a number of studies show that TSH levels begin to rise at relatively low iodine levels in the 1,700 mcg/day range. 
I am not trying to be insensitive toward someone trying to boost their testosterone through what they see as a reasonable alternative, but I just do not see the wisdom here. For example, let's take a hypogonadal male that has total testosterone of 300 ng/dl who starts megadosing iodine. He might get a boost up to 450 ng/dl. Now that increase is a nice increase, but it is probably not going to make that much of a difference for him. And he is risking hypothyroidism and goiter for this relatively small boost.
So why do iodine fans do it then? Well, there is some grey and poorly understood areas of the research. In fact, the evidence seems to point that some people can consume extra iodine and be affected less than one might expect. In fact, there is even one study of northern Japanese seaweed workeers, who consume a lot of seaweed - between 50 and 200 mg/day!  Of course, this is about a 1,000 times the RDA and yet the prevalence of goiter is only about 6-12%. Of course, that is a high rate of goiter, but pro-iodine advocates like to point out that hypothyroidism is not common there, a fact that has baffled the researchers.
Again, though, there is ample research that megadosing iodine can cause problems. For example, a number of studies that show high iodine levels in the diet can really causes problems. One study of Peace Corp volunteers in Ghana found that 44% had goiter from excessive iodine in their water filters. When this was taken care of, their "mean serum iodine decreased from 293 Â± 306 to 84 Â± 46 Î¼g/liter."  And, correspondingly, their TSH dropped from a high 4.9 to a very sound 1.8 mU/liter.
So, to me it seems like risky business to consume extra iodine. One of the partipants in the above-mentioned forum had her rheumatoid arthritis flare up when she took 15 mg per day. It got worse from there:
"At about 20 mg per day, my throat starting closing in. I didn't know it at the time but it was a goiter developing. At 30 mg per day, I experienced very scary double vision, heart palpitations, light headedness, cold tingly numbness in my head and nausea" 
Better safe than sorry...
3) Kenneth L Becker 2001, Principles and Pracice of Endocrinology and Metabolism, p. 957
4) The Journal of Clinical Endocrinology & Metabolism December 1, 2002 vol. 87 no. 12 5499-5502, "Effects of Chronic Iodine Excess in a Cohort of Long-Term American Workers in West Africa"
7) Journal of Andrology, May-Jun 1988, 9(3):215-219, "Serum Levels of Total Testosterone and Sex Hormone Binding Globulin in Hypothyroid Patients and Normal Subjects Treated with Incremental Doses of L-T4 or L-T3"