Some of those flaws are there because the Trilogy went through many script changes, and some of the scenes were filmed when scripts that were different from the final one were being followed.
As you know, people here often find those earlier scripts and post relevant pieces. One of those earlier scripts had Roth arranging Frankie's survival. FFC dropped that part of it from the final cut, probably because it was too far-fetched. But what if "Michael Corleone says hello" was filmed when the earlier script was being followed--and FFC left it in inadvertently? Or because Tony Rosato intended it as something Richie the bartender could tell the cops--"I dunno who done it, but they said, 'Michael Corleone says hello.' " That'd set the cops on Michael's trail, and further besmirch his "legitimate" reputation.
This isn't the only example of film snippets from earlier scripts that were left in the final cut, even when the earlier script was changed. Last year, one of our sharp-eyed colleagues spotted Questadt in Cuba--sitting right behind Roth at the businessmen's meeting with the President. There was absolutely no logical reason for Questadt to be in Cuba. And, if Michael had spotted him sitting right behind Roth (and he would have, since he was in the same room), Michael would know that he "belonged to Roth" and would never have perjured himself when Questadt turned up as the lawyer at the Senate hearing. Sure enough, another colleague here posted a section of an earlier script in which Michael and Tom talk about meeting Questadt way before Cuba. That script was changed, probably because FFC saw that there'd be vastly greater drama in the way it played out in the final cut. But he left the two seconds of Questadt in Cuba in the final cut, probably because he liked the way the scene played, didn't want to or couldn't reassemble the actors to re-shoot that scene, or simply didn't notice that Questadt was still in it. In any event, he certainly never envisioned the sharp-eyed people here!