There's one thing about the book that still puzzle me. After meeting with all the Heads of Families in the USA, Don Corleone go back home to have a meeting with his Caporegimes and Tom Hagen. Then the two Caporegimes leave and Hagen stays alone with Don Corleone. To take the direct quote from the book, I still wonder what was that "one dark fact" no one mentionned.

Direct quote from the paper back copy on page 297 Book V:
"But now he(Hagen)was sure that in the subtle and complex mind of Don Corleone a far-ranging plan of action was being initiated that made the day's happennings no more than a tactical retreat. And there was that one dark fact no one mentioned, that he(Hagen)himself had not dared to ask, that Don Corleone ignored. All pointed to a day of reckoning in the future."

Can anyone can clarify my mind on what was implied by that "one dark fact"?

Welcome, Machiavelli! Your excellent question shows that you took good care in choosing your nom de plume.
A guess is that the "dark fact" that Hagen dares not ask is: What role does the Don intend for Michael when he returns to America from Sicily? A clue is found a bit earlier in the passage that you cited:
The Don asks Hagen if he disapproves of anything the Don did that day. Hagen says no, but he adds that he doesn't believe the Don is not interested in why Sonny was killed, or in avenging him. It's "not true to [the Don's] nature." Hagen says the Don has "constructed a magnificent riddle." The Don seems enormously satisfied that Hagen has made that analysis.
I infer from this passage that, while the Don gave his word not to avenge Sonny, he didn't constrict Michael. To that point, Hagen might have viewed Michael's murder of Solozzo and McCluskey as a necessary expedient to save the Don's life. Now Hagen's dreaded question is: Does the Don intend for Michael to take over the family? And will Michael--his little brother, the college boy--now act in cold blood to avenge Sonny?

Thank you for your insight, Turnbull. I was suspecting that it had something to do with how to deal with Carlo Rizzi since he was proved to be a traitor. Like, do we get rid of him now, do we wait? If so, wait on what? But I was wrong.

You could be right, Machiavelli, since both Hagen and the Don knew that Carlo was responsible for Sonny's death. Therefore, a "dark fact" possibility was that Connie would be widowed and her child(ren) made fatherless.
I think part of the confusion stems from Puzo's inaproppriate use of "fact." "Fact" implies something known. But in the same sentence, it's also something Hagen "dares not ask." We don't "ask" "facts." Therefore, I assumed it's really a "dark question": Will Michael take over the Family? Will Michael avenge Sonny in cold blood?

Hi!

This is an excellent question.

I think that Puzo put the word "fact" in on purpose, but neglected polishing up the second part of the sentence - thus it was indeed a fact. Then, it is pointing to the day of reckoning in the future - so it implies revenge. Finally, Tom didn't dare to ask - which means that the revenge would be really terrible.

From this, my first impression was that the answer would have to do with Carlo's participation in setting up Sonny - but I must admit that this petty matter wouldn't bother any Don but Don Vito. Next I thought that there remained the difficulty of "proving" Mike's innocence - again, it's a private Corleones' affair. In my opinion, the question of succession is not a matter of a public discussion either - so it must be something else still.

For now this nice puzzle has been scheduled for batch processing in the long afterhours - and I may be back with another guess any time.

Best regards.

Alexander