Though Asimov wrote more Foundation novels, the first three books won a Hugo Award (an Academy Award equivalent for sci-fi and fantasy) in 1966 for best all-time series. But more than 50 years later, it’s hard to see why (especially when it was up against The Lord of the Rings). The novels do not rise above their serialized origins, with the individual parts of each book so distinct from one another as to seem like separate works crudely collated. They burn through a succession of stock characters, only a few of whom register in any meaningful way, and who are easily forgotten once they serve their purpose in advancing the narrative. Ultimately helpless in the face of psychohistory’s plan, most of them are rendered passive and interchangeable actors, mostly mere witnesses to the Foundation’s triumphs. As Seldon states in one of his pre-recorded messages, he has engineered their fates such that they “will be forced along one, and only one, path.”
This is odd because the things being criticized are standard science fiction patterns. Many important science fiction works have a serialistic structure -- e.g., A Canticle for Leibowitz, arguably the greatest science fiction novel of all time, is serialistic in structure. Asimov's characters are lightly sketched, but none of them are "stock" -- a stock character is a character structured as a literary stereotype who doesn't rise above a stereotype, but most of the characters in the first three Foundation novels are fairly distinctive if you compare them with characters in other texts. And science fiction is not typically character-focused. I think it may have been C. S. Lewis who noted that science fiction stories often suffer from excessive character-work. This is not to say, of course, that there aren't great characterizations in science fiction -- Miller's Canticle or Stapledon's Sirius come to mind as novels that do well in this regard -- but in the Aristotelian elements of story, science fiction is primarily distinguished by Thought, not Character, and there are major science fiction works, like Stapledon's Starmaker, that can only be said to have characters at all in the very broadest sense. And, of course, the early Foundation novels by their very topic necessarily share more with sweeping-history science fiction like Starmaker than with character tales. It was conceived as a science-fictional Decline and Fall of the Roman Empire, after all.
Likewise, it's odd to criticize the characters as passive when this is the point -- it is in fact explicitly the point of the first part of Foundation and Empire, in which the characters are quite active trying to subvert the Empire, all of which is entirely irrelevant, because they fail to understand until it's too late that the Empire's weakness is the combination of economic deterioration and unavoidable civil-military instability. Asimov's stories are very often puzzle-stories of one kind or another, and that was precisely the solution to the puzzle presented by Bel Riose: How do you stop the Empire's most talented and incorruptible generals from invading you? You don't have to do anything, because the Empire will stop him the moment he begins to look too successful; from the perspective of an Empire in decline, a successful general is always a more obvious danger to the Empire than barbarians beyond the borders. It all reminds me a bit of when some feminists attacked Ursula K. LeGuin's works for having female characters who were too passive -- LeGuin was, in broad terms, a Taoist, so the whole point of the stories that were being attacked was that being too eager to act and achieve was a poisonous temptation that often leads to self-destruction. The characters -- even characters like Bel Riose who are fairly well rounded for the brief time they are on the stage -- are not the point of the story.
Butler likes The Mule best of the characters in the original trilogy; that's a defensible taste, although my preference would be for Preem Palver. But he claims that he gets the fullest backstory of any character in the trilogy, which is again odd, since we get only a very sketchy backstory about him. Ducem Barr probably has the "fullest motivation and backstory of any character in the Foundation series", at least if we are talking about the original trilogy. (Of course, if you had the prequels, Seldon gets the fullest motivation and backstory.)