The question contains an interesting slippage, between the idea that "our current understanding of reality is flawed" and "our basic scientific method is flawed." Clearly, we need to be careful here to separate the substantive from the methodological. It goes without saying that all of the findings of quantum physics mentioned in the question were discovered and documented by the scientific method.
That being said, there are some points where quantum physics may run into methodological difficulties in terms of the scientific method. Since the scientific method depends upon the notion of "controlled observation", quantum effects that are themselves dependent upon the process of observation cannot, by definition, shed any light on the unobserved behavior. Put in simple terms, if observing a particle necessarily has an effect on that particle, there is (necessarily) no way for us to know what the particle is like in its unobserved state.
On the other hand, this is of very little concern in the bigger picture of things, because these quantum effects are only relevant at absurdly microscopic levels. If you are dealing with anything the size of an atom (or, better yet, everyday phenomenal objects), this stuff just doesn't matter.
So, the end result is not that the scientific method is flawed; rather, that it has limits, and that it is possible for us, at times, to brush up against those limits.