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One potential problem would be certain beliefs which say 3% of brilliant physicists believe to be true and the rest believe to be false. For such a belief the smarter you are the more likely you are to believe it's true, and the more likely to believe it's false. This is because the only people that believe either way are brilliant physicists.

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This is an excellent point -- I was going to say something very similar to this. I certainly agree with the above post, but I would actually take it farther than this -- let's say that the 3% of physicists believe in a theory which would (if correct) invalidate something that everyone else believes is obviously true -- not something they merely don't have an opinion about (for example, that time moves at the same rate for everyone/everything, or that all meter sticks measure the same length for everyone).

Such a theory could say some very great things and solve other problems (which cause 3% of physicists to find the theory to be absolutely compelling), but simply turn out to be wrong.