Opening with children and Seldon's vault was unexpected, but a good 'hook' for people who are not hard-core fans.
Making Gaal Dornick female was maybe done just to give a gender balance that was not normal in the 1940s. That Asimov adjusted for later, and it is inherently a good idea.
But for those who don't already know how it comes out, having the young mathematician female increases the feelings you must have for her plight.
Also done tastefully - the Empire is abstractly cruel. No one is seen being tortured, which matches the original short story that Asimov wrote as a lead-in when the original short stories were collected as three books.
Incidentally, I'd have seen two books as better. The first half of the second book completes the main theme, and its second half introduces The Mule and mental control.
What we have are a lot of extras built around that short story. Including religious extremism, a present-day reference but also one Asimov would almost certainly have agreed with. And they have the good sense to make the religion of Gaal's planet not even remotely like Islam: insulting moderate Islam is no way to discourage extremism.
The jump-ship adds imagery not found in Asimov, as well as protection for passengers. But it seems an excellent extra.
The image of the transit is very obviously derived from what astronomers think a Black Hole would look like. And which matches the images from a distant galaxy seen in 2019.
The Genetic Dynasty is a nice innovation. In the Asimov story, the nominal Emperor is an unseen child and the man with the real power is behind the scenes. A man who negotiates with Seldon, but much less dramatically,
Viewers should have noticed that the person listed as Demerzel is very odd and strangely powerful. Readers of the later Foundation books will know why this is perfectly proper. I will not spoil what will later emerge.