I understand your concerns, however: As Yuval already pointed out, there is no guarantee that numbers from noisy real world systems are "better" for your application that the numbers generated from a pseudo-random number generator.
IID random variables are a mathematical idealization. Simplifying a little bit, for every real physical system and every random number generator there is a statistical test that will reveal that the generated numbers are not IID. The "bad" random number generators are those where such a test is already known, the "good" ones are those where such a test is not known. In particular, every pseudo-random number generator will generate numbers with some kind of correlation. The question is, if the generated artefacts will produce wrong results when your application eats them. In this sense, all random number generators are "bad", but with regard to a specific application, some will produce artefacts and some will not. In practice, it is most often not possible to determine which random number algorithms will produce artefacts for a given application, and which won't. So, the best advice that I can give you is
1) Use random number generators only that pass the usual statistical tests. Don't use implementations that you don't understand.
For tests for random number generators see e.g.
2) Run your application with at least two different random number generators.
"Different" means of course different algorithms, not e.g. two different linear congruence generators. This will give you a good fighting chance that the results that you get aren't artefacts of your random number generator.
William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery: Numerical Recipes, The Art of Scientific Computing (3rd edition, chapter 7)
James E. Gentle: Random Number Generation and Monte Carlo Methods (Springer, 2nd edition)