These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Foreshadowing: The creation of Gaia/Galaxia is foreshadowed a couple of times.
On his death bed, Elijah advises Daneel to look at the big picture, which parallels Giskard's notion of the Zeroth Law.
In a conversation with Emperor Cleon regarding the emerging attempt to establish a legislative government for Trantor, Seldon expresses sympathy for the idea of democracy, but concedes that it is impractical for such a huge population as Trantor has (much less the entire Empire). Daneel (who among other things would serve as Cleon's first minister under the alias Eto Demerzel, and would act as a benefactor to Seldon) undertakes the creation of Gaia with the idea that if he could turn "humanity" into a concrete concept, and eliminate issues like social status, then it would be possible to make decisions about what benefits humanity as a whole without being limited by weighing individuals and groups relative values against each other.
Hilarious in Hindsight: ".... people had no real conception of the fact that the Empire was running down. They had been more or less running their own affairs since the Zeonian revolt..."
Narm: Hardin shouting "The Galactic Empire is dying!" No wonder one Encyclopedist called it a "hysterical" statement.
The original version is even more narmy, with Hardon declaring "If you ask me... The Galactic Empire is going to pot!" Asimov wisely changed this bit of dialogue to something more dignified.
Rooting for the Empire: Since Asimov was thinking in terms of a grand future history where there are no such things as "heroes" and "villains", there are plenty of "villainous" characters who still come out as capable, sympathetic people in opposition to the heroes:
The original Galactic Empire itself is still worthy of admiration:
The Committee of Public Safety in charge of internal security on the Homeworld, Trantor, exiles Seldon and his followers to the edge of the galaxy... but recall that he had 100,000 people following him and he's been actively telling everyone who will listen that the Empire will fall. The Committee is simply desperately trying to keep galactic civilisation running. Exile seems remarkably civilised in comparison to what even a modern state would do to its dissidents. In fact, for another three hundred or so years, the Empire, still civilised and infinitely better than the barbarous kingdoms the Foundation faces out at the periphery, is actually the first port of call for some of the heroes through the series (who need to be in the space of a power the Foundation respects.) The Foundation is, after all, an aggressively expanding nation, and its methods of control over other star systems have included theocracy and plutocracy.
General Bel Riose wants nothing more than for the Galactic Empire, now in serious decline two hundred years after Seldon's death, to become strong and great again. He is saddled with a traitorous second-in-command and a suspicious Emperor, and up against an enemy that possesses more powerful technology than his own (although his own resources are just sufficient for the task, as he is a military genius.) In a normal space opera, he'd be the hero.
The Mule is The Woobie and has a sympathetic backstory. At this point in its history, the Foundation is a fascist Hereditary Republic that is crushing the freedom of its independent traders and citizens alike. The Mule's empire, in comparison, is well-run and free (as long as you don't try to topple his government.)
The Foundation itself, in the novels Foundation's Edge and Foundation and Earth, represent the last desperate attempts by normal humans to maintain their free will and liberty. Not everyone wants to be in a Hive Mind, or in the alternative, ruled by a cabal of elites with psychic powers. Although the fact that Mayor Branno wants to play Galactic Conqueror and rule the galaxy from Terminus simply means the loss of liberty to a non-psychic imperial regime.
Shaggy Dog Story: At the end of Foundation and Earth, it is revealed that the Foundation was nothing more than Daneel's backup plan, enacted during a time when he was having trouble setting up Gaia. Since Gaia is now operational and about to take over the galaxy, the Foundation and its history was ultimately irrelevant.
... Or not. The 'about to' is still indicated to be something that will take a long time yet, enough time for the Foundation(s) to keep things running in the meantime, and it is implied that the transition from Gaia to Galaxia will take advantage of the infrastructure — mental and otherwise — established by the First and Second Foundations. It may have been a great deal less important a story than what seemed to be the case previously, but it wasn't irrelevant.