Question: Suppose there is a physical theory that predicts that the observable physical laws differ when applied to the observer himself rather than to the other people, for any given observer. 

Would existence of such theory invalidate the applicability of scientific method?

I am referring to [a paper by Thomas Breuer](https://homepages.fhv.at/tb/cms/?download=tbDISS.pdf) where he has proven that an observer in quantum mechanics cannot measure certain parameters about himself or a system that includes himself, even if he can measure similar parameters of other people. This means his own wavefunction appears differently to him, a phenomenon which Breuer called "subjective decoherence".

So my question is whether this result disproves usefulness, credibility or validity of scientific method?

Answer: 
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> So my question is whether this result disproves usefulness, credibility or validity of scientific method?
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It would problematize the scientific method **only for those cases where results are not repeatable through controlled observation**.

Most (if not all) mysterious quantum effects disappear at the level of everyday objects, so the odds of these kinds of things actually causing a practical problem for science as it is routinely practiced are vanishingly small.
It is no problem at all: once you have discovered that you can't measure things, you ask other people to do the measurements for you. This happens *all the time*. Maybe you don't have the right camera, or you don't have a particle accelerator, or you use a CCD camera instead of your eye to capture some photons.

Also, those phenomena for which a human-sized observer is entangled with observables of other systems are extraordinarily limited, given how big human observers are. So this particular theoretical point is of no interest physically.