Twice in this chapter the narrator tells us he stands next to a "crazy cannon" while watching a football game. How might this prove to be important?

Holden makes a reference to the crazy cannon, which was he says:

"in the Revolutionary War and all" (Salinger)

Holden tries desperately to find things wrong with Pencey Prep, he must find fault with the school, or else he has to blame himself for being kicked out of yet another school.  So he is characterizing this school, as he has other schools, as full of phonies.  He does not believe that the cannon was in the Revolutionary War, he feels deceived by everything that Pencey represents.

He tells us in this chapter that the ads for Pencey are misleading, suggesting that all students at the school play polo.  He resents the idea that the school represents itself as having the ability to mold young men. This is definitely phony, he did not get molded into anything, he is still the same, failing academically and getting kicked out.

Holden trusts no one, and he certainly is not going to believe that the cannon is real, the football game to Holden is considered way too important by the school and the students are expected to really get into the spirit and root for their school.

Holden won't buy into this, he is standing up on the hill, next to the crazy cannon because he won't mingle with the other students in the stands because he won't engage in school spirit and fun.  He proves his point, because he was the manager of the fencing team, and while they were on there way to a match in NYC, he left the equipment on the subway.  He won't take responsibility for this, and feels picked on by the team.  This is more evidence that Holden is immature and unable to accept responsibility for his mistakes.

Holden tells the reader that while he is standing next to the cannon, he is trying to feel a connection with the school.

"Anyway, I kept standing next to that crazy cannon, looking down at the game and freezing my ass off.  Only, I wasn't watching the game too much.  What I was really hanging around for, I was trying to feel some kind of a good-by." (Salinger)

Holden reveals a great deal about himself in this first chapter, he tells us that he cannot feel, he is numb, he is so depressed that he is unemotional, unable to feel an attachment to the school and that scares him.