2 things...

1) After Vito calls a meeting with the heads of the five families to reason together and make peace, he tells Tom that he didn't know until that day that it was Barzini, not Tattaglia, that killed Sonny. How did he know this exactly?

2) Along with that, the scene where Michael and his father are talking in the garden, and Vito is telling Michael that someone in the family will betray him and will set up his assassination...How did Vito know that Barzini was gonna try to kill Michael? (Especially after Vito agreed to put up political protection for the drug rackets, and they had made peace.) Did Barzini sense that Michael did not share his father's sentiment about not breaking the peace they made? Could someone clear this up?

At the meeting, Barzini took the lead.

Barzini had already broken the peace. It's a natural consequence of such relationships that Barzini coveted the Corleone empire and Michael's death would hasten his acquisition of it. That's why a traitor was needed.

Correct on both counts Olivant. When Vito agrees to the compromise, Tattaglia is practically whining to Barzini about whether Vito will eventually seek a vendetta.

Agreed. At the meeting, Barzini sits at the head of the table. After Vito gives his explanation of why drugs will be the ruination of the Mafia, Barzini replies on behalf of the others. When Vito appears to make a concession, Barzini jumps right in: "Then it is agreed--the traffic in drugs will be allowed and Don Corleone will give it protection in the East..." And modern Barzini is the only Don smoking a cigarette--the Moustache Petes are puffing DiNobili's.

The scene in the garden with Vito and Michael occurred after the scene in which Tessio complains that Barzini is moving in on his territories. So it's no surprise that Vito would conclude that Barzini will be the one to make the move on Michael.

The only mystery is: Why didn't Vito know earlier that "it was Barzini all along"? As he told Tom, "Tattaglia is a pimp...alone he could never have outfought Santino." Tattaglia had always been a pimp--didn't Vito know that before the meeting? And, shouldn't Vito have known that Barzini was the number-two Don, and that he'd have the most to gain from the drugs deal, and from eliminating Vito?

Because the Don, rest in peace, was slippin.

He probably figured as much, but don't forget that it wasn't long ago that he was lying in the street gravely wounded. His intuition wasn't up to par yet.

I agree with all the posts previously made.

The Don knew that Barzini would make his move soon and probably use someone very close to get to Michael. It was the smart move and quite likely the strategy the Don himself had used back when he was on the rise. So it's not that he was gifted with foresight but just around forty years of criminal activity had given him some insights on such things.

As to whether he should have known it was Barzini sooner, well maybe. But the Don made very few mistakes. As Tattaglia had lost a son to the Corleones, perhaps it was reasonable to ass-u-me that it was Tattaglia that would be most vigorous in prosecuting the war.

It's not until the meeting where Barzini subtly takes control of the discussion that's it's clear to Vito who his primary enemy is. After Sonny's death it could be that Vito thought things through and realized that Tattaglia didn't really have the guns or the brains to go head up against Santino, but Barzini did. Again as others mentioned he was recuperating from multiple gun shots and was preoccupied with healing...

The other reason the Don might have been slightly slower to see Barzini's involvement was the Don's prejudice against such "dirty" businesses as drugs and prostitution.

Since Sollozzo was a former pimp and Tattaglia was deeply involved in pandering, the Don may have simply conflated both vices together and not seen past Tattaglia's involvement, for whom he obviously had no respect.

The Don might have had these thoughts:

"This narcotics business is just the sort of infamia a man like Tattaglia would be involved in. Barzini's no friend of mine but he's no fool either. He's too smart to waste his time backing a drug peddler like Sollozzo. But Tattaglia is greedy and stupid."

Another clue that it was Barzini al along was the deal they floated out to the Corleones after the two atempts on Vit's life failed. Sonny kills Bruno Tattaglia, and they offer to cancel it out very readily. I don't know that Tattaglia would be that forgiving about his own son, but Barzini....

In the novel, Vito says almost exactly that, after Tom briefs him on the upcoming meeting with Sol. He says something to the effect:
"Do you have it in your notes that Sollozzo made his living before the war from prostitution--as the Tattaglias do now. Write that down before you forget it." Tom is stung: he knows that Vito is "notoriously straight-laced on matters of sex," and fears that he will let that bias get in the way of ok'ing a deal that Tom has just touted as being good for the family.

That's a good point, dt. It was pretty grand of them to say that Bruno Tattaglia's death is tit-for-tat for Vito's shooting. Couldn't have been Tat's sentiment.

Contrast it with the movie's opening scene. Bonasera wants Vito to kill the two boys who ruined his daughter. "I ask you for justice," pleads Bonasera. "That is not justice," Vito replies. "Your daughter is still alive." Well, Vito was still alive after the shooting, but Bruno was dead.

"Is vengeance gonna bring your son back to you? Or my boy to
me? I forgo the vengeance of my son..."

I FORGO the vengence of my son. That line alone translates that in Vito's mind the killing of Bruno Tattaglia did NOT cancel out the attempt on Vito's own life, nor did it cancel out the taking of Sonny's life. Because if he felt that it did, then he would have never said "I FORGO" the vengence. Which makes me believe even more so that Tattaglia would never have been the one to agree that the attempt on Vito's life cancelled out the killing of his son. Tattaglia lost a son, Vito lost a son, but yet Tattaglia is even more worried that as time goes by and Vito's position becomes stronger, that he may attempt any individual vendetta for the killing of Santino. So if Tattaglia was really the one who originally agreed that the killing of his son cancelled out the attempt on Vito, than he surely wouldn't have been worried about Vito seeking revenge for the death of Sonny, because in truth, their both losing sons in the war cancelled out each other.

So it had to have been Barzini all along.

I wonder how Barzini got Tattaglia to forego the vengence of the death of his son for the mere prospect of a temporary peace? He had to have convinced him they were going to kill Vito eventually, I suppose, but it shows that Tattaglia was just a pimp who could have never outfought Santino.

Tattaglia more than likely feared Barzini and knew he needed him to survive. He would have been essentially a subordinate for this reason. In short---he was probably just following orders.

It may have had nothing to do with Barzini. If Tattaglia couldn't have outfought Santino, he surely could never outfight Vito.

it would have been such a big mistake for Vito really not knowing who is his real enemy, it makes me believe that line "it was Barzini all along" is much more a cool quote thrown in there than such an important statement. the Don had to know WAY before the meeting all the details about all that was going on with the families, or he wouldn't call the meeting in the first place. we just try to dissect the film and sometimes we still can not come up with an explanation - "Michael Corleone says hello"...

Vito probably means that the meeting served to show him in front of his face how Tattaglia was really just a subordinate for Barzini, like it was already said, "whining to Barzini", and accepting the role of Barzini as the counterpart of the great Don Corleone. that's probably why Tattaglia just had to swallow the death of his son.

Initially I believe Vito saw Sollozzo as a kind of free agent asking permission of the families to set up his drug operations in New York. Barzini, who was an old time Moustache Pete was probably richer and more powerful in his earlier years, and Vito probably overestimated his wealth as well as understimated the rising power of Barzini. It served Barzini's interests to use
Tattaglia as his front man because then he could wet his beak in the drug business, increase his strength and eventually take over.

It probably would have been more appropriate for Vito to have said that he was absolutely sure until today that it was Barzini all along. But then again, all the families are eternally plotting against each other. To pick one out regarding a particular plot might be challenging.

Right.

I think maybe Vito knew that it was NOT Tattaglia all along, but wasn't 100% sure who his hidden adversary was until the meeting.

The Corleones are in open warfare against all the other families. So I think Vito's comment about it being "Barzini all along" meant that Barzini was the driving force behind both Sollozzo and Tattaglia as well as being the boss with the muscle and smarts to take on Sonny and win.

Barzini (and Sollozzo) were the up and coming modern mafiosi.
As other posters mentioned elsewhere, probably Barzini hoped that Vito would see Tattaglia's involvement with Sollozzo and go for the deal, not looking any deeper than that.