In the opening paragraph of the story, Holden says that he doesn't intend to reveal about his parents because
...my parents would have about two hemorrhages apiece if I told anything pretty personal about them.
This kind of hyperbole is often heard in conversations of adolescent boys. The reader realizes that Holden is young, undisciplined, inexperienced, and fully intends to tell his story in his own words rather than writing a traditional novel in the manner of works like David Copperfield. J. D. Salinger may be writing a novel, but his narrator is just writing a sort of informal memoir.
Holden exaggerates again when he says that his brother D.B. bought a Jaguar
...that can go around two hundred miles an hour.
This was around 1951. An English-made Jaguar could not possibly go more than 120 miles an hour, and there would be no roads available at the time on which anyone could drive even that fast.
A little later Holden talks about a football game in progress.
It was the last game of the year, and you were supposed to commit suicide or something if old Pencey didn't win.
This exaggeration shows Holden's disaffection for Pencey and for schools and school spirit in general. He is a misfit, a loner, a rebel, a cynic, a skeptic, an introvert.
Holden shows he is interested in girls. He talks about the headmaster's daughter, Selma Thurmer, who
...showed up at the games quite often, but she wasn't exactly the type that drove you mad with desire.
This is an example of understatement, in contrast to the exaggeration of the previous examples.
Pencey was full of crooks.
This is an obvious exaggeration. In the first place, Holden would have no way of knowing about the misdeeds of all the boys in his school. But the word "crooks" suggests men who are real criminals, either white-collar crooks, or hoodlums, or gangsters. The boys at Pencey who did things such as misappropriating Holden's gloves were not even delinquents but selfish and inconsiderate of others, which is not exactly atypical of adolescent boys.
Only one example of false information is fairly obvious in Chapter 1. This is in Holden's description of the "crooks" at Pencey.
The week before that, somebody'd stolen my camel's-hair coat right out of my room, with my fur-lined gloves right in the pocket and all....Quite a few guys came from these very wealthy families, but it was full of crooks anyway. The more expensive a school is, the more crooks it has--I'm not kidding.
It is false information to say that Pencey was full of crooks and also exaggeration. It is false information to say that "the more expensive a school is, the more crooks it has." Holden does not have enough experience with enough schools to be able to make such a broad generalization.
Holden seems to be exaggerating when he says:
After I got aross the road, I felt like I was sort of disappearing. It was that kind of a crazy afternoon, terrifically cold, and no sun out or anything, and you felt like you were disappearing every time you crossed a road.
It is noteworthy that Holden is completely alone throughout Chapter 1, although he mentions a number of people. He seems lonely throughout the entire book, so it is appropriate that he should be introduced not only alone but, as he says, "ostracized." It is freezing cold and he is standing all alone on top of Thomsen Hills next to an old cannon from the Revolutionary War. He is something of a revolutionary himself.
Everything William Delaney mentioned above and this one:
"It's really ironical, because I'm six foot two and a half and I have gray hair. I really do. The one side of my head--the right side--is full of millions of gray hairs."
This information is exaggerated because despite mentioning that he looks older, he is often questioned about his age. When he meets the prostitute sunny, the first thing she says to him was in regards of his age. When he wanted to buy alcohol in the bar, the bartender was suspicious and asked for an ID before he would serve the alcohol.