Bell's Inequality

Help me out here. I buy the whole party line about QM having never made an incorrect prediction, which I’ve seen stated countless times. (Most recently on Nova’s Elegant Universe.)

Is Bell’s Inequality an incorrect prediction of QM? As in, is QM predicting the “hits” should be fewer than experiments show?

Also, I’ve never really bought several of the assumptions built into Bell’s Inequality. First off, the very nature of uncertainty seems to invalidate the assumption of “if I had done so and so, such and such would have happened.”

And secondly, why is the basic arithmetic involved even appropriate?

No astounding insight here, just dropping a few links.

Bell’s Theorem disputed on grounds of dubious initial assumptions.
Bell’s Theorem defended on grounds that the premises in question play “an entirely trivial role in both the formulation and the proof of Bell’s theorem.”

Cool, thanks. That’s basically exactly what I was looking for.