I get that Prof. Diamond is trying to answer the big questions of "why?" some civilizations invented "cargo" (material goods) and others didn't. I have not read the book, and just watched the first episode of this miniseries.
A lot of the details of the argument ring true to me. The worldwide distribution of beasts of burden, types of farm crops and weather patterns all certainly have an effect of the rise of civilizations. But this can't be the whole story, or even the major part.
When showing Diamond interacting wit the New Guinea folks, the emphasis was on the New Guinea struggles to get food. Hunting is inefficient, and farming is difficult labor due to the crops and lack of domesticated animals. Okay - but what was really striking is what was the lack of a written language. At the end of the episode, Diamond says something to the effect that if only geography had been different, then the New Guineans would have invented the helicopter, and not Westerners.
The problem with this argument, is that in order to invent a helicopter, you must first understand fuel, energy, materials, densities, air molecules, physics, weather, and hydraulics, just to name a few things. I agree with Diamond that the New Guineans are plenty smart to understand all those things, but in order to generate knowledge, a society must have a physical way to disseminate knowledge (scrolls, printing presses, paper, etc) and culture of acceptance of new ideas (criticism of new ideas is fine, indeed necessary to refine knowledge). Diamond didn't discuss the role of culture at all, and this is a huge omission.
Ultimately any theory of the rise of civilizations can be supported by cherry-picking data. This is a historians job, not a scientific endeavor. Diamond has his theory, and any number of people have their own theories. I personally don't find Diamond's theory to be very compelling.