Whenever someone repeats straw man statements like that, I've found it pretty predictive of ignorance of the subject combined with personal bias. Perhaps that is the case here?

"You cannot accurately predict how long today’s trends will continue."
Irrelevant. First, you don't have to predict all trends, just the ones that carry significant influence. Second, in the made up world of the Foundation series, it takes place some 50,000 years into the future. We, today, have a very short history to work with. The vast majority of that history is poorly documented at best.

Assuming non-total collapse, and the relative ease of preservation of the data, even a hundred years from now we will have a better picture of trends, attitudinal shifts, and events than we do for 20 years ago. While I do enjoy saying that never in history has doing so little been so well documented, the fact is that to an historian or a psychologist or sociologist (or indeed an anthropologist), that data can be mind blowing.

In this postulated society of Asimov's mankind has hit a particular type of zenith. We have tens of thousands of years of history collected for quintillions of people. Science has reached a rather specific state, and in a sense devolved in a rather specific way. I won't give too much away because I don't want to spoil it for the potential new reader here. But if you have read both the Foundation and Robot series, do read them again with what I am saying here and you'll see what I mean.

"You cannot accurately predict what new trends will emerge, or when they will do so."
Again, there is historical and statistically based good reason to anticipate that with sufficient data size and population size we can predict trends - as we gain both today we gain more predictive power, there is nothing to indicate this will suddenly stop. It might, but where that point is is not something we can say given our infantile amount of data and population. Again, you don't have to predict a specific trend, or what it looks like exactly.

"You cannot accurately predict when “known bounds” will be violated. (Example: Trump.)"

Trump wasn't a violation of the known bounds. Many of us did predict Trump's victory, but before that we predicted the role Trump filled. Just because the self-serving mass media relied on self-serving polls, which are the basest of measures and barely qualify as scientifically reasonable let alone terribly accurate, and thus failed does not mean the rest of us are equally ignorant. But, once again, you don't have to predict a known bounds' violation.

If you can predict the trend, and have access to the right levers, you can alter the course earlier and avoid it. This reduces the problem of bounds violation to a much smaller frequency. For example, Trump could have been avoided entirely by Romney beating Obama. The conditions needed for Trump's rise to power would not have come into play because they do require specific conditions. While Trump himself is not cognizant of them, a part of his "gut" knows this by his frequent flirtations with the idea having led to naught until this last cycle. He is, after all, primarily an damned good opportunist.

"You cannot accurately predict when “black swan” events will occur, or what they will be."
With our limited data set of a small population over a short span of time, you are correct. However, given fifty thousand years of data for quintillions of people in billions of scenarios, I think it would be foolish to insist that we would still be in the same state we are today. After all, that would be quite the prediction, no? More to the point, one could argue that Hari Seldon (the Raven) was a black swan event. Thus if you can't predict them (which is true but only for a limited window), then you can't say that a black swan event can't happen to realize the underlying causes of them. The assertions of your argument are self-contradictory.

Many "unpredictable" things are obvious in hindsight, and it is precisely this hindsight feature of humanity (more broadly termed "experience") which produces our "gut feelings". If our hindsight covers say, only a hundred years and black swan events happen roughly every fifty years we do not have enough data on what produces them or indeed how frequently they occur. But over a thousand years of data could change that. Fifty thousand years even more so. These events are unpredictable because we don't have enough of them to analyze.

"You can limit the bounds of large group behavior only in a dictatorship, and only temporarily."

Shh, spoilers. That said to the broader point, you are incorrect. You are thinking of government action only. As someone else here mentioned, don't underestimate the power of controlling religion. And given it arises so early in the first book, it isn't giving away much to point out that this isn't an incidental comment but one specifically germane to the series at hand.

And now for a brief, related aside. The U.S. Army knows how to recognize riots before they occur. It also knows how to prevent them with nobody but those moving the levers knowing what happened. This is a provable fact. Is it in the larger view a short term prediction and application of stimuli? Absolutely. But compared to the timeframe of the event and the population, it is actually remarkably over-capable. Nor does it require dictatorial actions, nor does it require the people undertaking the actions to know what is going on. Now extrapolate that ability forward.

If you know how to prevent riots, and you have the means to control the levers to stop them, what power do you have? You have the power to dramatically alter the public perception with little effort. You have the power to set the stage for riots you want, while preventing the ones you do not want. That is a tremendous power to limit the bounds of the equation.

To bring that into a modern context: the riots in Charlottesville (yeah, that was a riot) were specifically preventable. I've written elsewhere on some critical aspects that would have prevented it, but more to this point is that despite these there are still functional inflection points that have been determined through statistical analysis and observation of how riots form. The further from an event you are, the smaller a given action has to be to alter the course. The day of the riots the U.S. Army (functionally speaking; legality is separate) could have stepped in and prevented the riot. Indeed they could have done it without being obvious about it, or with general knowledge of the public.

One could argue we are currently careening toward a violent conflict in this country, centered around authoritarianism, race, class, or some combination thereof. If one were to see this and organize action to prevent it, or to enhance it, one could do so through "riot management". You don't stop ones you think lead where you want, and you stop ones you think counterproductive. One could argue that to do so isn't predictive because you're actively controlling it, and semantically likely be correct. But that would be to ignore that the models used were actually predictive.

"You can predict what will happen in response to various stimuli, but you cannot make accurate long-range predictions of who will apply this stimuli, when it will be applied, what other stimuli will be applied by other people, and what outcome will result from the application of competing stimuli."

Again, given a limited data set, this is true. The accuracy of a given predictive model is founded by not only the methods, assumptions, and assertions, but also the quality and quantity of data being drawn upon. For our short known history humanity does indeed follow certain patterns, some to the point of annoying repetition. There is nothing at hand that says we would not do so in the future.

"You can pay attention all you want to trends and tendencies, but there is no way you can extrapolate 10,000 years of future history from them."

If I had 50,000+ years of actual history to analyze that would likely change. But, once more, you are assuming that it is only prediction. Again, while I do not wish to spoil the series for the new reader what I am about to say is in the very beginning of the first book: Asimov's fictional psycho-history wasn't solely predictive, it involved active alteration and management of the conditions. It was not ignorant of free-will, it specifically incorporated it by initiating action to specifically alter the trends of a future.

Indeed if you recall the foundation of the story you would also recall the Empire had been in existence for over a millennia. I would assert that the likelihood that mankind had politically, sociologically, and economically "fallen" into a routine set of patterns in order to make that happen are pretty high. In the preceding millennia a Galactic Empire was able to be maintained absent psycho-history. That is not something that has ever happened in human history to this point. I think it quite likely that humanity would have to be rather narrowly limited in some fashion regarding politics, social interaction, and economics to accomplish that whether by conscious means or by relatively stable patterns evolving. In this fictional future it was not a result of a conscious control of humanity but a result of a mind bogglingly large collection of patterns, trends, and events. Frankly, I'd be disappointed in humanity if we couldn't look back at that and see the patterns using hindsight.

Further, your throwing out of 10,000 is a rather disingenuous amount of straw given that right in the first book the predictions with specificity are for a mere 300 years into the future, with granularity decreasing beyond that. It seems rather short-sighted to think that with fifty millennia of history a prediction at a large scale of a few centuries is impossible; especially when actions are taken to influence the events.

But nonetheless, to get back to the original discussion: L. Neil Smith has been proven incorrect on his assertion that because we can not accurately predict a given individual's action we can not predict group behavior. We have, in modern psychology, quite an array of tools that are quite predictive. The nihilistic postmodernists that currently occupy our intellectual strata and political positions certainly object to them, but that doesn't alter the effectiveness of them. To what degree we can do that at an even larger scale and with longer timeframes to analyze is open to debate. But to say that because we can not predict an individual we can thus not predict a group of humans has been thoroughly falsified both theoretically and empirically.

Even historically and linguistically we can see this is false. Humans developed "labelling" or grouping of people because they serve as general predictors of behavior. Labels and groups are short cuts for thinking, but they exist because they were/are useful. Indeed, the inverse of what Smith asserted is true: that you can predict a group to behave a certain way does not mean you can predict the behavior of specific individuals in the group. It is in this aspect that current society is screwing itself over: the over-application of group labels to make conclusions about individuals that are (or are perceived to be) a member of that group.

Now don't take any of this as an argument that we can "use psycho-history" today. As an astute reader would note, I actually argue the opposite: we lack the data to do so. Nor does that mean it is a given that development of psycho-history will happen (well, in a specific universe). I am merely pointing out that to say that in the world so envisioned it actually makes no sense, and that to say it is impossible given those conditions is folly.