Answer

Hello,
I’ll write briefly, off the cuff. First, the Lubavitcher Rebbe’s approach is well known (like that of most Hasidim): that the contraction is not to be understood literally. He opens the article with this, and that itself is of course complete nonsense. Simply foolishness.
A few comments on what he says about science (in his order):

1. What he derives from the various fields can be learned even without all that. The lessons seem fairly simple to me.
2. The claim that science describes the “what” and faith answers the “why” is a common claim (although I think the Rebbe really is one of its early sources), and it is also fairly correct (though one has to be precise about the difference between “what” and “why,” because there are some kinds of “why” that science does deal with). But as long as this is not demonstrated, it remains a slogan. In my books I showed this in detail in several areas.
3. Popper is far too minimalist an approach to science; nowadays no one takes it seriously (that is, the idea that falsification is the only thing possible in science). Thomas Kuhn usually talks nonsense, and he is not a philosopher but a sociologist.
4. The truths of faith do not come from the soul any more than scientific generalizations come from it. Some of them come from the tradition we received from Sinai (without the human interpretations later added to it), and the other part—all the later additions to it (which is almost everything we have)—is open to error just like all human thought, and certainly more so than science. Science at least tests itself empirically, whereas the axioms of faith do not subject themselves to empirical testing. That is, they do not even meet Popper’s minimal condition. Therefore, when there is a contradiction between a scientific finding and a fact we received by tradition, my personal inclination is in favor of science.
5. Lice on the Sabbath is an excellent example of what I wrote in the previous section. The Sages decided this on their own judgment (apparently in light of the scientific knowledge of their time), and therefore there is no reason in the world to assume they were right and look for excuses for why observation did not show otherwise. If it had been a tradition from Sinai, I would consider thinking that science does not know the whole truth on this issue (which of course may be true). But why assume the Sages knew more? From their souls? I have no confidence in that as an instrument for recognizing scientific reality.
6. What he says about cud-chewing animals does not really stand the test of the facts. It takes rather convoluted apologetics to explain what the Torah says on this matter (and here this is really the Torah itself, not an interpretation by later people, so here I would indeed consider such convoluted interpretations).
7. I will not elaborate here on my attitude toward Hasidism.