In a nutshell, Saul wrote a pamphlet of very arbitrary opinions and misrepresentation of history (even recent history) that led him to pathetically wrong predictions.
Saul claims that "twenty years ago" the democratic world got divided between the Left and the Right. He seems to lack even the most basic knowledge of the history of post-war Europe. Italy's first elections (1949) were "ferociously" (to use his term) divided: the Communist Party won just a few votes less than the Christian Democrats. Both France and Germany had strong Leftist parties that eventually won the elections. The ideological split that Saul refers to was born in 1945 with the advent of true democracy. The USA was the last western country to experience such a split, during the Vietnam war. Saul seems to think that a phenomenon is born only when it reaches the USA. (I guess he thinks that Islamic terrorism was born in 2001...)
As he discusses the "West", he never mentions the obvious fact: that ethnic, linguistic and religious barriers were broken down in 1945. Before 1945, there was no united "West" to talk about: just western powers that were fighting each other anytime anywhere. He later refers to the ideological West as a "handful of countries". How wrong was he proven to be. The whole of Eastern Europe has joined the "West", and the whole of the Far East is joining the "West". In fact, it seems like the entire planet is moving towards integration with the "West". One could wonder what exactly is "not West" after the fall of the Soviet Union?
He claims that "the century ends much as it began". How embarrassed must he have been on the 11th of september 2001. He totally missed Islam as one of the key new elements. But it is not the only one: how about the European Union? The century began with the European powers fighting each other anytime anywhere, and it ended with the European powers united in one federation. That is probably the single biggest political change in the history of the world since the fall of the Roman Empire. How about China, that began the century as a weak failed state and ended it as the second world power? How about India that ended the century as an economic power after being a poor colony for so many centuries? How about Eastern Europe, whose countries are now among the fastest growing economies in the world and, oddly enough, staunch allies of the USA? How about the USA itself, that began the century as a second-class power, with no empire of its own, and ends the century as the world's only superpower, with soldiers deployed in all continents? How about France and Britain that began the century as world empires and ended the century as small countries the size of Italy or South Korea, and much less relevant than China? Did "the century end much as it began"? Or was it just the opposite?
Even on smaller issues, Saul is chronically inaccurate, mainly because his knowledge does not seem to extend beyond his backyard. He claims that deregulating the airline industry led to "fewer airlines flying to fewer places at higher prices". Obviously, he has never stepped into any of the London airports and has never travelled to the continent. One can now fly to many more airports at much cheaper prices (sometimes one tenth of the old price). The working class is now able to fly anywhere in the world, something that was unthinkable before deregulation started. Where in heaven does Saul live?
Saul claims that we live in a world that does not question authority. This contradicts his previous assertion that the USA has never been so divided, and one wonders how he felt after the two George W Bush elections, probably the most divisive events in the history of the USA after the Civil War: is the USA progressing towards less or more dissent? He also seems to ignore the peace marches of the Sixties, the 1968 student riots in Europe, and, today, the generation that reads Noam Chomsky, watches Michael Moore's documentaries and votes for Ralph Nader (millions, not dozens, of people).
Saul claims that we are building the largest weapons market in the history of the world. I guess it depends on his definition of "weapons market". The Turks defeated the Eastern Roman Empire thanks to cannons that they purchased in Europe (lots of them). Milano became a wealthy city thanks to their cannons, which they mostly sold abroad. What is unique about today is that there are so many independent countries: in the old days, when very few nations were independent, the market of weapons was limited to a few powers, but, as a percentage of GNP, was much larger (up to 75% of France's budget at one point, versus the current 14% in the USA).
Saul claims that the USA has become constitutionally incapable of winning wars, "capable only of losing". Maybe so. But most observers believe that the USA won in Afghanistan and Iraq wars that the West had not won for thousands of years. And the real issue now is not winning wars (the USA has proven that it can win any war anytime anywhere) but winning the peace, a concept that Saul completely neglects.
Many of his statements are merely sensational and rarely justified. They often sound like he was inspired by Mao's old "Red Book": propaganda disguised as wisdom. Someof them are indeed cute: "Like all religions, Reason presents itself as the solution to the problems it has created". It is not justified anywhere (are we really sure that moving from caves to skyscrapers is a "problem" and not a solution?), but it "sounds good" as a sentence to quote in your next book. Elsewhere, though, this gets really annoying: "The most important capital good produced in the West today is weaponry" (he never provides data to back this seductive statement, which is in fact false); "Never has failure been so ardently defended as though it were success" (meaningless, right? and maybe it could be applied to Saul's very book); "Fighting is the most ancient and consistent of the organized arts" (with all due respect, I think that both hunting and religion, and perhaps even cooking, came a lot earlier, but, again, he doesn't bother to explain why he thinks otherwise).
Some of his statements are also plainly false. For example, he mentions a 1986 terrorist attack in the Quartier Latin of Paris that killed 150 people: there were a string of bombs, but I don't recall any bomb that killed more than 4 or 5 people. For example, he claims that "the more the USA and Canada modernize their mail delivery, the less mail they can deliver at a slower rate to fewer places". All the sources I check prove the opposite: mail was never delivered faster in history. There has been a decrease in mail delivered only after the advent of e-mail, but that happened after Saul published his book and for reasons that are totally unrelated to his argument. (He also claims that the French postal system works better than the USA: obviously he has never lived in France. Also he neglects to mention that France spends a huge amount of money subsidizing its postal system, and postage is much more expensive in Europe than in the USA). So many false premises would cast a shadow on his conclusions even if he had used logic to justify them.
It is preposterous to claim (in the chapter on "Specialization") that today's individual is so absorbed in her/his job that s/he can't have broader view of the world, as if in the past the artisan of Florence or the peasant of France or the coal miner of Germany, who worked 16 hours a day six days a week, had any time for political, philosophical or scientific speculation. It is misleading to claim that today's philosophers and scientists use a specialistic language that only an elite can comprehend whereas in the past "Descartes, Bacon, Locke adn Voltaire did not write in a specialized dialect: they wrote in basic French and English and they wrote for the general reader". He forgets to mention that in those days very few people knew how to read and write. Thus Descartes was read by only a few thousand people all over Europe, and Locke by a few more in England. Their specialization was... writing, a specialization that was exclusive to an elite. So many superficial analyses weaken whatever conclusion he reaches (and it is never fully clear what Saul advocates: abandoning Science and returning to the Stone Age? forbidding Physicists from discussing theories that the ordinary man cannot understand?).
Saul's analyses basically amount to a long series of 20/20 hindsight (telling us that some doctrine failed because... it failed) and provide precious little advice on how to improve the "system", maybe because he would become vulnerable to the same kind of criticism that he wages against everybody else.
His book is ultimately a virulent attack against the rule of technocrats. Over and over again, Saul tries to paint technocrats as heartless, cynical hypocritical idiots, and regrets that technocratic societies have "eliminated the humanities". He forgets to mention that, not so long ago, there were regimes that loved the humanities, that were actually crazy about studying the classics and paying tribute to past glories: Hitler and Mussolini are the most famous ones. They, too, hated technocrats, no less than Saul does today. A little earlier in time, cardinal Richelieu founded the French Academy, the supreme example of a state sponsoring the humanities: very few of us would like to live under Richelieu's regime, though.
All in all, Saul seems to be pathetically out of touch with his own age. His book mainly happens in his own mind. His book belongs to fiction, not to historiography.
For a book titled after Voltaire, Saul spends very little time explaining the causes of the Enlightnement and, most importantly, why it happened in France (and not, say, in Spain, a country that had a similar regime). Had he done this bit of research, Saul might have realized how shaky the foundations of his theories are.