"The interesting thing about such a value is that it could be used to determine the correct value of any problem simply by casting it to the appropriate data type."

This is incorrect. Determining the superposition's state won't give you the correct answer. It will give you a random answer from all of its possible states -- weighted by the chance of that being the right answer. This makes quantum computing much trickier.

http://scottaaronson.com/blog/?p=208 is a great article if you want to understand how some Quantum algorithms we know of will work using this "probable-answer" property.

I always wonder about experiments like this: exactly how certain can we be that the calculations aren't simply producing the theorized result because the calculations assume the theory (directly or indirectly) to begin with?

It's a subtle point, but I think it's something that should always be double checked. How do we know that our mathematical equations apply in all simulated situations, and that they don't break down under different circumstances? What assumptions are we making about reality, and how sure are we that they remain true under the circumstances being calculated?

IANAP, so I really have no clue how to begin answering these questions, but I think they should always be asked.