Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person (Omniscient) and First Person (Peripheral Narrator) who pretends to be Third Person
Let's start with "Franny." The narrator is some unknown third party observing Franny and Lane's rather tense date. What's interesting about this narration is that when the text gives us information on the characters, the narrator often dodges omniscience and guesses at the characters' feelings based on appearance. If the narrator were truly omniscient, he or she could just go into the characters' heads. Example: "Lane watched her for a moment with mounting irritation. Quite probably, he resented and feared any signs of detachment in a girl he was seriously dating" (Franny.2.34). That "quite probably" is the key phrase here. You'll find that this sort of "omniscience-dodging" is a hallmark of Salinger's short stories.
Of course, the far more interesting point of view to discuss is Buddy's narration of "Zooey." We talk a lot in this Shmoop guide about how insular the Glass family is, how closed off these siblings are from the rest of the world, how alike they are and how they're really only understood by one another. It makes sense, then, that only a Glass could narrate a Glass family story – no one else would understand or be privy to it in the first place.
Choosing Buddy as the narrator also provides the opportunity for some of that "literary exhibitionism" (to borrow a term from The New Yorker) for which Salinger is so well known. To place Buddy as the narrator is to severely complicate the story and to add dimensions to our interpretations of it. As a tiny example, consider the layering going on in the bathtub scene: Buddy tells the story of Zooey reading a letter written by Buddy in which is a haiku composed by Seymour. Or consider the phone conversation at the end of the story: Buddy narrates Zooey who's pretending to be Buddy while Franny repeats what Zooey said to her earlier that night. The boundaries between these Glass siblings are being blurred – where does one end and the next begin? It's a fitting question, considering that Seymour's ideas have been appropriated by his younger siblings, and Franny is now re-living the same "act-or-not-to-act" crisis that Zooey underwent four years earlier.