The moon landing
The social narrative about the moon landing is laden with braggadocio, and Sammler hates this situation. He hates that the culture celebrates technological advances while ignoring the military component of that progress. As a Holocaust survivor, he knows that not all technology is good technology. For instance, gas chambers were a technological advance that he absolutely detested with true horror. The moon landing symbolizes the public blindness to that risk.
The family unit
Sammler struggles to accept the difficult nature of one's family, because his family was stolen from him by Nazi forces, and most died. Then in America, there is an intense focus on dating and marrying the right person and sacrificing for a better life for one's family. To Mr. Sammler, this is somewhat inappropriate, because he sees a kind of unfortunate consumerism in this approach. Sammler thinks of family with deep pain and loss.
The American Dream
Mr. Sammler also resists the American Dream and those who obey those ideas. By hoping for more pleasure and luxury, Sammler believes they are simultaneously weakening their selves, which might come to bite them if their survival ever depends on adaptation again. The American Dream is a cultural narrative that has powerful effects, but Sammler feels that in general, it is accepted without scrutiny.
The prestigious job
Mr. Sammler has a position of considerable authority, because he has tenure at Columbia University, but that doesn't mean to him what it might to other people. It doesn't make him feel any emotional security, nor does it make him crave more power. In fact, he feels like he is actually quite powerless to make the kinds of changes that he wants to, because it is hard to make someone face the risks of life when they are focused on luxury and achievement. It is an ironic symbol of his powerlessness.
The planet through his eyes
The titular Planet is Earth, of course. The title is itself symbolic, because although the planet is shared with all the human's, to Mr. Sammler, it is an experience all his own. His point of view is symbolized as the entire experience he has with the earth, which symbolizes the nature of subjectivity and true knowledge. The subjective truth that Sammler knows with certainty is the likeliness of human suffering, which he learned in a horrendous way, by surviving the Holocaust while all his family died.
