Why did he even bother, since Pentangeli was "small potatoes" and all? Plus, when Michael visits Roth in Miami, he tells him of his plans to kill Pentangeli. If Roth was under the impression that Michael was going to kill Frankie anyway, why would he go ahead and order the hit himself?

Roth planned to get rid of Michael after getting his two million dollars, so he did it for a back up plan. He figured if for some reason his plan to kill Mike in Havana fails again, he get him in the US with those senate hearings. He decided to have Frank killed in a way to make sure Willie would get the message so he would cooperate with the FBI to testify against Mike. Frank accidentally survives and goes with the witness protection plan of the FBI himself to get Michel because he thinks Mike has double crossed him. Mike really didn't want to kill Frank when he told Roth about killing him, he mostly wanted to see Roth's reaction toward the matter.

Along the same lines, but a little different.
If Roth planned to have Mike killed in Cuba, he would take over Mike's operation in Nevada.
Frankie, the head of the Corleone Family in NYC would then start agressions against the Rossato bros. By whacking Frank, and I do not feel they were trying to implicate Mike with Frank or his men, they would rid themselves (Roth and his allies) of a potential adversary.

Plus by clipping Pentagili, they would weaken Mikes power outside of his home base in Nevada.

The plot is complex, but if you bear with it, it'll make sense:
Roth chose to kill Michael after Anthony's First Communion party because he knew Frank Pentangeli would be there, contentious over the Rosato Brothers, whom Michael and Roth favored over Frankie. Thus Frankie had the perfect motivation to kill Michael--and would make the perfect fall-guy for the crime. The assassination attempt against Michael failed. But when Michael visited Roth in Miami, Roth was heartened that Michael, as he expected, blameed Frankie for the attempt. He promised to kill Frankie (“Frank Pentangeli is a dead man”), and even asked Roth's permission (“You don’t object?”)! Ah! Roth saw a silver lining in the cloud of the botched assassination: Michael would kill the obstreperous Frankie without his having to lift a finger or spend a dime! Heh-heh! BUT:
Instead of killing Frankie, Michael dispatched him to settle his problems with the Rosato Brothers. Oh-oh! Roth knew Michael would never give a pass to a mortal enemy. Now it was certain that Michael didn't suspect Frankie in the Tahoe attack—leading to the possibility that he did suspect Roth. SO:
Roth ordered the Rosatos to kill Frankie at their meeting. That way, he'd eliminate Michael's chief NY ally before the two of them could cook up any mischief against him. To maintain his façade, Roth could always claim that he’d only done what Michael said he was going to do anyway. (Later, in Havana, Roth implied that Frankie’s assassination was tit-for-tat for Michael’s murder of Moe Green.)
Bear in mind that Roth intended for the Rosatos to kill Frankie in that bar, and for his pal Batista to kill Michael in Havana. But when both failed, Roth improvised brilliantly: he reached for the Senate lawyer Questad (who belonged to him) and arranged for Frankie's survival to be kept secret. That way, Roth (through Questad and the Senate committee) nearly trapped Michael into going away for five years each on five counts of perjury.

Sounds good Turnbull except:

When Pentangeli is about to be killed the Rosato bros. say "this is from Micheal Corleone" Later in the movie it's made clear that it was kind of a setup so that Pentangeli would think Micheal had tried to kill him. Why else would they have said that (this is from Micheal..) if they were going to actually kill him? Micheal didn't really have anything to do with the murder.

in other words, I felt the idea was that Roth wanted Pentangeli to think that Micheal was trying to have him killed so that Pentangeli would go to the FBI when the murder attempt failed.

When Tom Hagen tells Micheal that Pentangeli is still alive he says "Roth set the whole thing up" or something along those lines. The thing that doesn't make sense about that though, is that when the police officer comes in they all start shooting at each other, if it was just a ruse nobody would have gotten killed and the whole scene would have been faked to make Pentangeli think the police had intruded during the attempted murder. So then the question becomes: Who was in on it and who was not?

Marcos, the issue of why Carmine Rosato said, "Michael Corleone says hello" if he intended to kill Frankie, is one of the two or three most-often-posted issues on these boards:

The simplest explanation is one that has been uncovered by Godfather scholars in an interview with Danny Aiello, who played Carmine Rosato. Aiello admits he ad-libbed the famous line, and Francis Coppola permitted the ad-lib to remain in the film. I believe FFC allowed it because it fit the plot, even though Carmine intended to kill Frankie all along. “Michael Corleone says hello” was intended not for Frankie-—but for Richie, the bartender, whose ginmill was being used to set up Frankie.
It’s obvious that Richie is a “civilian,” not a Made Man, and he’s nervous as hell about his bar being used for a murder (“Carmine, NO, not HERE!” he screams after the cop enters and Rosato draws his gun). Carmine knows that Richie might be squeezed by the cops investigating Frankie’s murder. Richie would be too fearful of Carmine to identify him as the killer. Still, as a civilian, Richie is not bound by the code of omerta. So Carmine hands Richie something he can give the cops so that Richie can get off the hook: “The murderers said, ‘Michael Corleone says hello.’ ” That line would set the police after Michael, and would be picked up by the press-- another nail into the coffin of Michael Corleone’s “legitimacy.”

Why would the bartender have testified against Michael? The only way the FBI got Pentangeli to testify is that they had so much stuff on him that they could have put him away for a long time. I would have thought that the barman would have kept his mouth shut to avoid trouble.

Turnbull great posts, as always, but I am not sure about the theory that the comment was for the bartender's benefit. When the cop walks into the bar, he treats the bartender like a friend, and assumes he is the proprietor of the place, asking him whether he is open or closed. The bartender lies to the cop saying he just came in to clean up. This means the bartender probably was in some way connected to the Rosato brothers, so he may not have been a complete civilian. It is also likely that after this incident he lost his liquor license. I have always thought that Roth staged this in a way that Pentangeli would live (who knows...maybe the cop was dirty as well and he timed his entrance to make it apppear like he was inadvertently coming in to look around. Certainly the cop would have been among the first to see the half dead Pentangeli, and could well have taken measures to get him some medical help, at which point the FBI took him into custody. I agree that the Senate hearings were a sort of "Plan B" for Roth after the Havana assassination plot failed. I think he probably took some delight in his telling Michael it was revenge for Moe Green, knowing all the while that Pentangeli was alive.

There is another thing at work here, which I don't think anyone has talked much about, and that's Willie Cicci. He is last seen in the street getting hit by a car. Obviously he survived because he was the first witness to testify ("yeah the family had a lot of buffers").
This means he was also in some kind of protective custody, and it means that Michael must have believed that he was also dead. I guess he didn't care much however, because there may not have been much that Cicci knew.

Question for Turnbull: Isn't it much easier to give the link to one of your 100 posts/answers about this question? Or at least copy the former answers?

My guess is that Hagen, acting as Michael's lawyer, was told, by the committee that Cicci would testify. That would have been part of their plan to lull Michael into lying under oath: "Oh, they've only got Cicci? S**t, he doesn't know anything. I'll lie."

Okay, Richie is indeed a civilian. He runs a bar in a Mafia neighborhood. He probably pays protection to the Rosato brothers. So, he knows that in such a neighborhood he could be a dead man for any number of reasons even as simple as serving one of the Rosato brothers the wrong drink let alone squealing on them about a murder. (Along those lines, I've always wondered why the cop in the bar doesn't hassle the Rosatos. You mean to tell me that a beat cop in that neighborhood doesn't know who the Rosato brothers are?)

Anyway, regarding the dynamics between Roth and Mike. Yes, Roth was going to kill Mike from day one. Through Ola he compromised Fredo and he backed the Rosato brothers against Pentangeli. Why? Because Pentangeli ran what used to be the Corleone family which, I guess, Joey Zasa eventually took over. Remember, the Rosato brothers were probably based on the Gallo brothers who rebelled against the Profacis (Clemenza) and then Joe Magliocco (Pentangeli) on behalf of Gambino and Genovese(both Roth)whose real target was Bonanno (Corleone). So, anything that created havoc in the Corleone world Roth perceived as benefiting him.