Interesting ideas - Missionaria Protectiva, Race consciousness, The struggle for self-authorship, Role others play in the fulfillment of prophecy.
First 250:
Missionaria Protectiva and Bene Gesserit would have planted the Muadib prophecy in Arrakis for political leverage counting on Jessica to birth a daughter. So that she could be wed to a Harkonnen and through that marriage a son could be had. The son then could have fulfilled the prophecy if Freman loyalty was needed for their cause. [Dr. Kyne's thoughts]
Reverend Mother Giaus Helen was aware Paul showed promise of fulfilling their Kwisatz Haderach prophecy.
The dialog, motivations, actions, and interplay between the characters are realistic. (Maybe this is a given for books of this caliber).
The Duke unintentionally paid the way for Freman loyalty to Paul [as evident in Dr Kynes after thoughts on the Dukes visit to the Crawler Harvester]. Jessica paid way for the same with her Bene Gesserit cunning.
Second 250:
Paul is cold towards dukes passing.
In the still-tent, Paul identifies the part of his psyche that is prescient and mentat-like as a separate entity he calls 'the sleeper'. Through Paul's impulsive attempt to foil the guild banker's intention towards his house [following Jessica's insight], it can be assumed 'the sleeper' was driving him before his realization of its existence in the still-tent.
The Barron's desire to employ Hawat who had served the Atreides for 3 generations as his new mentat and to think he won't figure out yueh was the traitor is unrealistic.
Paul's prescience shows him probable futures that may come to past [Idaho was seen to stand with them in the desert in the vision he had in Caladan but he had died in the actual future that came to past].
Dr. Kynes and his father had worked on terraforming the planet in a way that would have seemed natural once the tipping point was reached.
Based on Jessica's confrontation with Stilga in the open desert, it can be assumed that in order to use the Bene Gesserit voice she must first read the target and then mimic the target's voice for the command to take hold. But the effectiveness may also depend on the susceptibility of the target.
Paul's decision to name himself Paul Muad'Dib instead of Muad'Db shows his need for authorship of his own fate.
Third 250:
Race consciousness and the struggle for autonomy; Paul dreads the future he sees birthing through him but grows more and more powerless to change it as the story moves along. Because of his struggle he becomes resentful, even toward his mother.
The duke's talismans, the bull's head, and the portrait of his father may have been an analogy of how he saw his father. As someone who faced the bull's horn instead of avoiding it. This may have been a driving force for him to not let his house become a renegade house and instead move to Arrakis to face danger.
Bene Gesserit breeding; Bene Gesserit puts stock in both genes and the upbringing when choosing males to take children from.
A reverent mother has access to memories of other reverent Mother's in her lineage and commune with them.
The Freman have some prescience abilities.
Paul succumbs to his fate.
It's unrealistic how fast Paul was able to figure out that Sardaukar come from Salusa Secundus when Hawat with all the mentat access he has had figured that out only 2 years after the Dukes death.
Fourth 250:
Alia can project her thoughts into Bene Gesserit and take some sort of control over their line of thought. This comes as a surprise to the reverent mother Giaus.
Alia is also able to leave thoughts in others' minds to be unlocked when they next think of her [Paul's thoughts after Alia is captured by the Emperor].
The spacing guild is in reality more powerful than the emperor or the great houses, but this is a fact that the Emperor seemed to have not known (contrary to how the relationship is depicted in the 1984 adaptation of the movie).
In the appendix, Frank Herbert ties the loose end of why the Bene Gesserit order didn't act on Paul and Jessica before they moved to Arrakis or before the fall of the Emperor by saying an order even higher than the Bene Gesserit that few were in on had a hand in allowing Pauls fate.