One deleted scene which I think was extremely important to part of the plot is the one where Michael arrives at the Corleone Mall after finding out that his father has been shot, and when he walks into the house, we are shown Thresa Hagen sitting alongside Clemenza, outside the Don's office. When Michael enters the Don's office, we see Sonny and Tessio sitting there talking. Now I don't remember the exact dialogue, so I am going to paraphrase a bit here.

Sonny tells Michael to leave, that he may not like what he is going to hear from him and Tessio. So Michael tells him " He's my father too." Sonny says something like " Pop would kill me if he found out that I let you in on this stuff." But Michael refuses to leave. Sonny then says something like " Ok college boy, you're so smart, who set up the old man, was it Clemenza or Paulie?" and Michael sits there for a moment and then says " Nah, not Clemenza, It had to be Paulie." and Sonny tells him, "Yes you're right, our man in the phone company confirmed that by tracing the calls from a phone booth across the street from pop's office." So that scene tells us that Sonny immedeatly suspected Clemenza, and that is why he had Clemenza sit out of that meeting between him and Tessio. They were deciding and trying to find out if Clemenza was involved.

Now again, I may not have the exact dialogue down pat, but that is basically what took place in that scene. It gives clarification to the later scene which shows Sonny telling Clemenza to take care of Paulie, because he set up the old man. Without that deleted scene we are left to wonder how Sonny came to that conclusion.