Lewis's Swollen Hand
While Lewis is guarding the ammo dump on the July 4th patrol assignment, Lewis's hand gets injured by some sharp nettles, and it begins to turn red and swell. This swelling doesn't stop on its own; it just keeps growing due to an infection, and Lewis doesn't seem to notice or want to do anything about it. Eventually a teacher rubs some lotion on it, and the swelling starts to die down. When he gives him the bottle, Lewis holds onto it for a few minutes before throwing it away, declaring that he's "not a Tinkerbell." His swollen hand therefore has a double meaning: it represents Lewis's drive to be a hard, tough man without dependence on anyone or anything, but it also represents the growing sense the reader has that Lewis might be mentally disturbed.
The Ammo Dump
The central scene of the novel takes place at an ammo dump on the Fourth of July, where the three men remain guarding it despite the danger that the nearby fire could cause it to explode and kill them all. This situation reflects Philip's view of the war and life in general; tragedy can happen in a single instant with no forewarning, and we just have to live despite this danger.
The Blanket Party
After everyone in the barracks realizes that Lewis is the barracks thief, they decide to have a "blanket party," meaning they throw a blanket over Lewis and beat him up. This blanket party is a symbol of retribution in a selfish world as well as of Philip's acquiescence to going along with anyone everyone else is doing. It's an unpleasant symbol, but one that's crucial for understanding Philip's character.
Philip's Car
When Philip leaves home to join the army, he gives his car to his younger brother, Keith. In doing so, he is implicitly giving Keith the responsibility of caring for their mother; since Philip is no longer around to help out, Keith needs to step up. Keith, however, doesn't accept the responsibility, taking Philip's car and ditching it in San Francisco, a symbolic abandonment of his family along with his physical disappearance.
Prince Valiant
While on crowd control duty, Philip encounters a young, attractive protester he mentally dubs "Prince Valiant." This man tries to persuade him that what he's doing in Vietnam is wrong, being understanding at first but becoming riled up, eventually giving the soldier the finger. This man is a symbol of the ironic nature of nonviolent protests - they're still cruelly effective and can have serious negative consequences, as seen through the anger and disillusionment of the men of the barracks after the protest.