From the article:

Of the various ways to critique science, the most fundamental addresses the scientific method, which emphasizes... c) the relevance of things (material reality) over all else (more accurately, it emphasizes a specific perspective on material reality, the only perspective that science recognizes as valid).

What do they mean, a specific perspective on material reality? What perspective? And what "alternative" perspective does science (probably rightfully) regard as invalid?

One problem with the scientific model is how it maintains and relies on a perspective of the world as a frozen (static) place.

Only true for when the things it's studying are static (like the laws of physics). Biologists certainly don't consider the world to be static.

Also problematic is the idea that everything can be broken down into discrete, quantifiable parts, that the whole is never more than the sum of its parts.

Again, untrue. Go ask a biologist if they believe that every organism can be fully understood in isolation from its surroundings. There are many disciplines where this is true, though (for example, chemistry).

Underlying both of these perspectives are the premises that the best or only way to know the world is to distance ourselves from it, to be outside of it; that this distance allows us to use the world; that utility is, in fact, the appropriate relationship to have to the world.

You mean that scientists often try to isolate the thing they are examining? Yes, that is to avoid any outside influence that would interfere with their measurements. But they never said anything about isolation being the proper way for humans to live.

On a practical level there is the understanding that scientists are operating within a system that is based as much (if not more) on hierarchy and funding as it is on paying attention to what is actually going on around us.

Then the problem is with capitalism itself, not science. Also, hierarchy is not the problem with society, it's the fact that this particular hierarchy is exploiting people.

The more subtle ones have to do with how we ask questions (“when did you stop beating your child?”), who we ask questions of (related to the questioner’s access, biases, language, etc.), what questions we think to ask, and how we understand the answers we get, as well as what meta-interests the questions serve (how are the assumptions of this culture fed and/or challenged by who, how, and of whom these questions get asked?).

If certain people are asking loaded questions, then the problem is that they're asking loaded questions. Still doesn't invalidate science as a whole. Also, what loaded questions are they talking about?

Western education predisposes us to think of knowledge in terms of factual information, information that can be structured and passed on through books, lectures and programmed courses. Knowledge is something that can be acquired and accumulated, rather like stocks and bonds. By contrast, within the Indigenous world the act of coming to know something involves a personal transformation. The knower and the known are indissolubly linked and changed in a fundamental way. Coming to know Indigenous [ways of knowing] can never be reduced to a catalogue of facts or a data base in a supercomputer; for it is a dynamical and living process, an aspect of the ever-changing, ever-renewing processes of nature.

I suppose now would be a good time to point out that just because indigenous people believed something, doesn't mean it's true. We support the struggles of indigenous people, because they have been slaughtered, and then forcefully relocated, and their culture was erased. But, that does not mean that everything that indigenous people believed was true. How is it possible for the "known to change in a fundamental way?" When I learned Newton's law of universal gravitation (F=GMm/r^2), I don't think I changed the law itself by learning it (and how could I?). Furthermore, I didn't change in a fundamental way. It was just one more thing that I then knew. Also, what indigenous tribe believed this?

it also continues christianity’s theme of a pure abstract and universal truth, separate from the sludge of everyday life, with scientists and doctors in the position of clergy that is, people who know more about us than we do.

Because certain things (again, like the laws of physics and mathematics) are pure, abstract, and universal truths. We now have accumulated so much knowledge on these subjects that it takes years and years of study to understand it all, something which most people do not have the time or motivation to do. So, when someone wants to know how black holes work, they can either get a PhD in physics, or they can have an expert explain it to them, and trust their explanation. Again, this isn't a bad thing, it's just a consequence of how much knowledge we've built up (and I'd say that's a really good thing!).

Some people believe in science (as something they don’t understand that can solve their problems) in ways similar to how others believe in god.

The difference being that science actually delivers.

Some people cite scientific references the way that other people cite scripture.

The difference being that scientific references are actually true.

Traditionally, science posits a neutral objective observer, a fantastical being to compare to any angel or demon: this neutral observer has no interest other than truth, which comes from information, and information is received inside of laboratories, with carefully identified variables and carefully maintained control sets.

Would you prefer scientists to not even try to be neutral at all, and thus come out with bogus results? This is supposed to be a criticism of science - if they aren't critical of this particular bit, then why bother mentioning it? And if they are critical of it, why?! Striving to be as neutral as possible when investigating something is good!

Science exemplifies this cultures tendency to specialize, and consequently to create experts, people who know every little thing about specific bits, but not how those bits interact with other things — clearly a result of thinking that is thing-based (vs. for example, relationship-based).

Once again, only true for certain fields, where what they're studying really is thing-based.

So for instance, practitioners of allopathic medicine prescribe multiple medications to people, frequently without having any idea about how these specific drugs will interact with each other

Yeah, I'm pretty sure doctors always ask if you're currently taking any medication before they prescribe you a new one. If you've ever seen commercials for a certain pharmaceutical drug (which are another problem with capitalism, but not with science itself), they'll always end with, "Do not take X if you are taking Y medication, or if you have symptoms of Z." They've thought it through, as best as they can.

much less any idea about how a person’s feelings or other life experiences are related to their physical health.

No, they also ask about that, but it's not a general practitioner's job to treat mental health problems - they'll probably refer them to a psychologist.

In other words, the inhuman aspects of totalitarian states are related to the reliance of those states on science as the ultimate arbiter of value: indeed, the idea that everything must be of measurable value is part of the scientific paradigm.

Guilt by association.

And I'm stopping there, partially because the next section deals only with anthropology, which isn't my field, and also partially because I'm getting tired of reading this.