You would think that after an event like this the authorities would have started to seriously going after the mafia. I don't think Vincent would have lasted long as boss.
IMHO, FBI should have gone after Michael, both for the helicopter massacre, to which he was clearly tied due to his checks lying all over the bodies, and for the Zaza thing. At the very least, he wouldn't have been allowed to leave US. Could have been an interesting change of pace, to see him being persecuted for something he didn't do
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As to the murders of the Andreotti look-alike, the archbishop, etc., not only was it completely implausible to organize all this on such a short notice, not only is it unclear how it would have gotten them back the half-billion dollars, but all the hell would have broken lose as a result, on all fronts. No way would they have been walking away from that.
I'd argue that that the previous 2 films skirt the suspension of disbelief, despite some notable lapses, but III just blows it up sky-high, which is one of it's most egregious short-comings.