One interesting thing Peter Biskind pointed out in his book "The Godfather Companion" is why did Michael have to ask Hyman Roth if it was okay to kill Frankie Pentangeli when it was his man and not Roth's.

After all, if it's within the family, Michael reserves the right to order a hit on someone or solve problems however he sees fit without having to consult with anyone, especially someone outside the family.

In a way, Michael set himself up by doing that, because it gave Roth license to make the attempt on Pentangeli and try to pin it on Michael...