I've been watching the spliced-together, deleted-scenes-included version of the Trilogy that ran on HBO recently:

--There's a seamless transition from the end of GF to Anthony's party in II. At the end of GF, when Kay asks Michael if Connie's accusations are true, and he denies it, Kay embraces him and gives him a guileless, trusting, accepting look. But, as soon as Clemenza kisses Michael's hand and Neri closes the door to his office, Kay has an awful, doubting look as if to say, "Oh, oh.." She follows it at Anthony's party: After Michael blesses Francesca's marriage to Gardner Shaw, Francesca tells Kay: "Uncle Michael is the most wonderful person in the world." Watch the look on Kay's face--"nope." Finally, after the Tahoe shooting, she's clutching Mary and shoots Michael an "if looks could kill" look, and Michael gives her several guilty looks.
--In the Francesca/Gardner Shaw scene, Michael, telling Gardner that he should take a course in business administration, shoots him two cheesy-smile-toothsome looks--very uncharacteristic for him.
--In the beginning of that same scene, you see a hulking youth in the background, wearing a plaid sports coat. In this version, the scene ends with Michael telling Tom, "Make sure her dowry is big: these people think Italian brides go barefoot." But, in the "Saga" version seen endlessly on US cable TV years ago, there's a 10-second extension of that scene: The hulking youth comes to Michael, and Michael says: "How's the football, Santino?" The youth replies, "Fine, Uncle Michael." The youth is Sonny's second son, Santino. We saw Sonny's first son, Frank, in GF, when he gives Vito a get-well card after Vito returns home from the hospital.
--When Connie brings her gigolo, Merle, to Michael in the boathouse, Michael denounces her and Merle ("You go with men who treat you like a whore...This Merle, I don't know what he lives on..."). But Connie speaks up bravely: "I need money." Watch how the camera shifts to Merle, who gives a patented whipped-dog look, confirming what Michael said about "...what he lives on."

No fan ever ceases seeing great stuff in the Trilogy.