It's an interesting and fun reading. Some of the facts are well-known but Glashow's interpretations seem biased to me.
Newton the tyrant
Most of us know that Newton was a kind of intensely assertive person. I feel that he had to be one, otherwise he couldn't have made all these important contributions. Isaac Newton was living in a world filled with non-Newtons and anti-Newtons, and it makes a difference.
Newton and accuracy
Newton was the first person who could have talked about all kinds of quantities - forces, masses, distances - in a quantitative fashion. He was surrounded by people who didn't appreciate the quantitative nature of physics. On the other hand, Newton really enjoyed to calculate numbers. So he just calculated them. Sometimes his numbers looked much more accurate than what could have been justified by observations.
But in his era, the rigorous prescriptions how to deal with uncertainties were not well-established. His numbers could have been incorrect but the moral lesson - namely that there are numbers behind these phenomena that could be determined very accurately and that fit together - was correct and extremely important. Newton was apparently trying to compensate the vagueness that everyone else was pumping into science.
Robert Hooke and others couldn't have approached all these questions properly because they lacked Newton's mathematical prowess. Unlike Sheldon Glashow, I don't think that it is a detail. A mathematical analysis of these phenomena is crucial.
And saying that the theory of planetary motion should be called the Newton-Hooke theory because Hooke has possibly explained Newton why angular momentum conservation (Kepler's second law) follows from a general radial force seems to be a dramatic exaggeration of Hooke's contributions. It's an important piece of the picture but there are roughly 50 comparable steps that one (Newton) must do in order to describe the planetary motion: deriving ellipses and their parameters from the differential equations.
Discoveries vs notation
Isaac Newton has also my sympathies in his calculus disputes with Gottfried Leibniz. Newton once wrote that Leibniz has invented symbols for his - Newton's discoveries. Newton's statement is oversimplified but at a rough level, it just seems this way to me, too. Of course that the notation is much less important than the actual mathematical content. Don't get me wrong: I think that Leibniz was an amazing polymath. But if you ask me who really made the difference among these two men, I wouldn't hesitate.
Newton hasn't discovered all theories of physics. More seriously, he had incorrect beliefs about some basic notions. For example, he failed to grasp the wave character of light even though there was some evidence for it, including important evidence produced by himself.
Well, motion of particles was very important for Newton because he has described and studied the laws that capture this motion. There were good reasons for him to think that such a setup could explain all phenomena in the world. Therefore, light had to be composed of particles, too. I find it legitimate that a certain amount of evidence should be ignored as long as it is important for keeping a robust theory of the world alive: the theory that all phenomena result from the motion of particles had some non-trivial evidence, too.
This strategy of Newton worked well in many other examples. He insisted that all possible phenomena obeyed his laws even though he had numerous opponents in every individual case.
His approach didn't work in the case of the character of light. Newton wasn't quite God. But I would only find Glashow's strong criticism to be legitimate if Newton were a candidate to become God. One more reason to sympathize with Newton is the modern discovery of photons: Newton's intuition that light can be described as a flow of particles was correct as long as a sophisticated enough theory is found.
Newton also believed that gasses are made out of static molecules that repel each other: that was his explanation of pressure. It was a sane theory to start with, too. Even though many details of these theories later turned out to be wrong, Newton's picture was relatively coherent.
Newton as inhibitor of British mathematics
Glashow - and Morris Kline - argue that Newton's heritage has slowed down British mathematics because British thinkers preferred Newton's geometric methods over Leibniz's continental, analytical methods. Well, synthetic geometrical and analytical methods are just two approaches to similar questions. Neither of them can be labeled as universally superior.
The British thinkers arguably became more geometric and "physical" but this allowed them to remain leaders in physics and engineering - electromagnetism, steam engines etc. The continental thinkers were focusing on mathematics and it helped to produce the great German-speaking mathematicians, among others. I, for one, think that this diversity was beneficial for the growth of mathematics and physics. To give Newton a minus sign for this influence is irrational. Moreover, it's strange to hear this conclusion from Sheldon Glashow who otherwise argues that the physical approach is more valuable than the mathematical approach.
More generally, the idea that Newton's authority is responsible for the relatively slow evolution of physics after his death sounds childish to me. The growth of physics was slower mainly because of two key reasons. One of them was that a large portion of the most important laws in the same "package" had already been found during Newton's life. The second reason is that the physicists who lived for 250 years after Newton were simply not the same kind of giants as Newton himself.
Moreover, the widespread idea that the opinions of Newton shouldn't have been contradicted because he was such an "autocrat of science" was a rational idea. If this paradigm were not followed, physics would be overrun by crackpots and the discoveries would effectively be "undone" a few years after Newton's death simply because everyone was a weaker physicist than Newton and they could have switched from physics to all kinds of myths.
It literally took more than 200 years before the new insights that physicists had collected became more important than the superiority of Newton's intellect. At the end of the 19th century, physicists could start to talk about Newton's misconceptions more frequently and more critically. It was a very good time for such a change. If they did it much earlier and collectively, physics would have gone to hell.
Newton has discovered all kinds of things, for example the formula for the velocity of sound, "v=sqrt(pressure/density)", although his original argument was not the most direct and the most comprehensible one (that's often the case in science that simplified arguments without useless components are only constructed later). But he invented ad hoc arguments to create the impression that his theory behind the formula agreed with reality much more accurately than it actually did.
Well, the details of his explained corrections were wrong but the qualitative message was correct once again. There are small effects that account for the errors. We know that they have something to do with non-isothermality of the sound waves. But a comfortable understanding of thermodynamics came much later. I find it very sensible that Newton had to find some plausible explanation of the small but measurable error. His theory was essentially correct but the numerical disagreement could have created a completely wrong impression that science couldn't have dealt with these things at all.
I have a full understanding for Newton's desire to make things agree exactly with theory. If a discrepancy can be measured, it's a problem. Because the world makes sense, these theories must give predictions that are exactly correct. Newton strongly believed that the world made sense exactly which is why it was more plausible to believe the first explanation of the discrepancy (he couldn't think of anything else) than to admit that there was an error.
Again, the qualitative conclusion of Newton is correct. The world works exactly. Today, all these things may be scientifically predicted and verified with accuracy that exceeds the accuracy accessible to Newton by orders of magnitude. I feel that Sheldon Glashow wouldn't care if science didn't work - even in principle - as a precise description of e.g. the phenomena at the Planck scale which is why he doesn't find quantum gravity i.e. string theory important. Well, I disagree.
Newton and creation
Sheldon Glashow criticizes Newton for believing that the world was created about 6000 years ago, as written in the Bible. What a heresy to think that the world was created if you live 200 years before Darwin! :-)
I think that Glashow's criticism in this section is entirely ideological and irrational. During Newton's lifetime, there was no good reason to think that the world had to be extremely old. The hypothetical distant past couldn't explain any detailed patterns of Nature and the creation billions of years ago was as (un)natural as the creation 6000 years ago. Geology was extremely primitive, evolution in biology was unknown, much like the Big Bang cosmology.
Why would an intelligent person choose to believe in such an old-Earth theory without having any good observational evidence if it seemed to contradict the history of mankind as known in his lifetime? I was brought up to believe and I still believe that the arguments in physics must eventually boil down to experiments and observations. What observations did they have to show that it was wrong to believe that the Universe was created to match some patterns explained in the Bible?
They had to start with a zeroth order estimate for the age of Earth. Newton started with the Christian estimate. The opinion that this is an illegitimate first guess is as much religion as Christianity: it is an anti-Christian religion. ;-) Newton simply believed that all the information in the Bible is relevant and hides important insights. It wasn't unreasonable because the Bible simply contained a non-negligible fraction of wisdom of his time: string theory textbooks were not yet sold.
Today we know that life was naturally created by billions of years of evolution. The Earth had to be around for billions of years and we know quite a lot about geology. The stars were created much earlier by pretty natural mechanisms. Three minutes after the Big Bang, nucleosynthesis provided us with the right mixture of nuclei. Inflation gave the Universe its huge mass. I could continue. The picture of an old Universe is supported by a lot of evidence, makes sense, and leads to a much more natural theory than the creation by Jesus' father. But the situation was very different when Newton was around!
Newton also predicted that the judgment day would come in 1867. It may have been a silly prediction. But even in the 21st century you can find people who predict that the world will approach destruction not in 200 years, as Newton argued, but in 10 years! And some of these apparently insane people could have been elected as vice-presidents of the most powerful countries in the world.
If we compare these two people, Newton was much more reasonable - because he has at least placed his prediction 200 years into his future - 3 percent of the age of the Universe in his setup.
His contemporary counterpart who is expected to know much more about science - because he lives 300+ years later - makes the same silly prediction but puts the end of the world to 2015. I just think that it is completely unfair to criticize Newton - the man who really introduced mathematics to the scientific discourse - for judgment days and fudge factor because many people, and not only those in the climate science, are doing the same or even more dumb mistakes today, too.
And that's the memo.