Salinger's word-choice is about as far from sloppy as you can get. There's a peculiarity and particularity to each of his phrases that conveys a seeming lifetime's worth of knowledge about characters who are present for only a dozen pages or so.
Consider his description of Teddy's speech: "Each of his phrasings was rather like a little ancient island, inundated by a miniature sea of whiskey" (2.1). Or of Mr. McArdle: "He had what might be called a third-class leading man's speaking voice: narcissistically deep and resonant, functionally prepared at a moment's notice to outmale anyone in the same room with it, if necessary even a small boy" (1.3). Teddy's physical appearance reveals the same peculiarity of phrasing: "The hole in the shoulder of his T shirt was not a cute hole. The excess material in the seat of his seersucker shorts, the excess length of the shorts themselves, were not cute excesses" (4.1).
Just by reading these passages, you probably begin to get a sense of the humor in "Teddy." It's by no means slapstick comedy, nor amusing puns, nor sarcasm. It is, once again, a very particular, Salinger brand of humor. You get the sense the author wrote it with a half-smile, and you're bound to feel the text tugging at the corners of your own mouth as you read. It's little details; Teddy, for example, uses the word "nephritis" in his diary and on the next page adds that he needs to look up "nephritis" in the dictionary. He tells himself to be nice to the librarian when the man gets "kittenish." The author tells us that the people in deck chairs looked up at Nicholson "as, perhaps, only people in deck chairs can look up at someone" (4.23). Hilarious? No, but certainly comic to a certain, peculiar, Salinger degree.