Are there flaws in (cryptographic) science/engineering/software/research due to pseudo random generators? I am trying to see if there were any incidents in the past where using PRNG or not actual random scheme leaded to wrong conclusion in research. 

For example, a lot of fields today use simulations to predict natural science results and I was wondering what are the best practices and if there were any flaws due to bad randomness in the past. 

For security purposes it's clear that one has to use encrypt lib random function, but for science or simulation of physical systems I am not sure it's the case. My guts say it should be the same, but I am not sure how to justify it. 

Are there flaws in (cryptographic) science/engineering/software/research due to pseudo random generators?
There are a few examples:


RANDU is probably the quintessential example of a bad pseudorandom generator. It consisted of the sequence $x_{i+1} = 65539\cdot x_i \bmod{2^{31}}$, which is always odd and whose sequential triples are highly correlated. It was implemented by IBM in its software, and so it was used all over the place. It has been suggested that research results relying on RANDU are not reliable, but I could not track down any concrete example of this.
Another interesting example is that of 1992 Ferrenberg et al., in which a pseudorandom number generator that passed the statistical tests common of the time, but nevertheless resulted in incorrect results in a real Monte Carlo Ising-Model simulation. The generator in question was R250, a very simple generalized feedback shift register.


There are most likely many other examples incorrect results that simply haven't been checked or reproduced.