A very interesting topic.
Sorry if my response is not a direct response to previous comments but there were too many walls of text and some of it were off-topic. (;
It is true that the scientific method, just like WHR said, has a flaw, but I would not call it "fundamental" but rather a pragmatic flaw.
As you may know the scientific method is a combination of inductive and deductive reasoning (the so called hypothesis + experimentation procedure). However, this means that the scientific method has some limitations to it. First, the scientific method is constrained by our technology. A caveman, no matter how incredibly intelligent he is, wouldn't be able to discover a quark since he doesn't have the technology to do it. Second, the scientific method is based upon statistical error and trial, and thus it can never prove something to be true. Heck, it can give us a very close answer but it is not necessarily the complete truth yet.
To illustrate this I will use the example of Galilean vs Relativistic transformations.
Galilean transformations is the common method to add velocities that we still use today for non-relativistic velocities. We now know that Galileo did not see the complete truth since we now know about Special relativity and the Lorenz factor. The reason Galileo would have never come up with this relativity is because he ever imagined there was a speed limit, nor had he a need to look for it. There was no need since relativistic speeds can't be seen on the Earth and thus his calculation were perfectly correct for that time.
Here is the flaw. Galilean transformations were considered to be truth since no one could defy his calculations since there was no experimental evidence to disprove him at the time. However, as we got deeper knowledge of light and relativity, we were able to disprove him. The scientific method bases its knowledge on "Working Models" and not necessarily truths. This means that scientific method can give us theories but not truths. It can only be disproved and never used to prove.
However, this flaw is not necessarily bad since we can use it to disprove previous theories and make them more complete just like the example.
