First, I just wanted to start with a quote that sounded like the father (Frank) but written by the son (Brian):
The only true path to survival of the human species lay as narrow as a razor, and slippery with blood. (Paul of Dune, p. 27)
I think part of why all of the pieces fit together better can be attributed to having read the end of the story and thus knowing what the most significant threat to the species is in that foggy future.
I really enjoy how the ornate knife that Shaddam had given to Leto I in Dune is an important link in the story. That link is not clear from reading only Frank Herbert's books and the most important part of the knife's history is actually explained in Paul of Dune. The first time we are reintroduced to the knife is on page 53 when Shaddam gives the knife to the head of his Sardaukar, Zum Garon, and tells him to find Count Fenring and give it to him as a gift. Shaddam's purpose here is to get Fenring to return to him on Salusa Secundus. Shaddam says that Fenring "will understand the significance" (Paul of Dune, p. 53). Recall, this was also the knife that Shaddam gave to Feyd-Rautha to duel with Paul Atreides at the end of Dune.
Another important story for which details are filled in is the story of how the Corrino family ended up on Kaitan when the seat of government and the Butler/Corrino family had been on Salusa Secundus for eons. To shed light on this, an important side story in Paul of Dune is about Paul's youth and the War of Assassins between House Moritani and House Ecaz which expanded to include the Harkonnens on one side and Atreides on the other. The first big clue was during a conversation between Viscount Moritani and his swordmaster Hiih Resser who studied with Duncan Idaho on Ginaz.
"This family was not always House Moritani. Once, we were named Tantor. After Salusa, though, every member of House Tantor was hunted down and killed. Every member the hunters could find, that is." (Paul of Dune, p. 141)
So first ... the name Tantor rings a bell! The Tantor family are the ones who fostered Xavier Harkonnen when his family was killed in a machine attack in history past before the Butlerian Jihad. Evidently, Baron Harkonnen did not know of this connection ... but we, the readers know. This quote from the Viscount leads to the assumption that there was some damnable thing the Corrinos did to the Tantors to provoke an act that left Salusa unhabitable for centuries.
Then another important piece of history which has to do with the Fenrings and the knife, but more importantly sheds light on the Tleilaxu-bred kwisatz haderach that the Tleilaxu conspirator Scytale refers to in Dune Messiah. All this relates to little Marie, the natural daughter of Lady Margot Fenring and Feyd-Rautha but who Count Fenring helped raise and train. Relatively early in the book, Lady Margot and Count Fenring meet with Reverend Mother Mohiam to inform the sisterhood that they will not be sending Marie to the school for training and that they are to be left to their plans which will serve everyone by assasinating Paul Muad'Dib. This part of the conversation revealed the arrogance and hubrous of the Fenrings:
Fenring also put an arm around the little girl. "The old ways of the Sisterhood have failed in spectacular fashion, hmmm? Now let us try ours."
"You would risk Marie's life in this enterprise?" Mohiam asked.
Lady Margot smiled. "Hardly. Our plan is perfect, as is our method of escape afterward."
(Paul of Dune, p. 201)
I need a little break from writing right now, so I will end this entry with a paragraph, provided as a chapter starter, which is from Princess Irulan's "Muad'Dib the Man".
Through those pivotal events, Young Paul watched his father prepare and respond with an extremism that some might have called ruthlessness. The ultimate lesson he learned from this, though, was that despite all of his father's retaliations, Duke Leto Atreides ultimately failed because he did not learn to be ruthless enough.
--Muad'Dib the Man by the PRINCESS IRULAN
(Paul of Dune, p. 278)