The biggest way in which Holden Caulfield shows himself to be hypocritical is the way in which he judges others so harshly but fails to apply those same standards to himself. Note, for example, what he says about Stradlater in Chapter 4 when he talks about what a "slob" he is and what a "phony":
Stradlater was more of a secret slob. He always looked all right, Stradlater, but for instance, you should've seen the razor he shaved himself with. It was always rusty as hell and full of lather and hairs and crap. He never cleaned it or anything. He always looked good when he was finished fixing himself up, but he was a secret slob anyway, if you knew him the way I did.
Holden is here incredibly harsh with Stradlater--he seems to hold him accountable for wanting to look good to others whereas in secret he is not so bothered with his appearances. This does seem rather hypocritical, as Holden himself does exactly the same when he goes out and meets with friends and acquaintances. He likes to look good too. In addition, note how, in Chapter 8, when Holden meets Ernest Morrow's mother on the train, he lies to her and gives her a false name, saying he didn't "feel" like telling the truth. It seems extremely hypocritical that Holden on the one hand judges others for telling lies all the time when he does exactly the same when he feels like it.