Cultural Identity
Pnin is always on the periphery, largely because his grasp of English is still very poor, and also because he just doesn't understand the ways of the west in general, and America in particular. This emphasizes the theme of cultural identity, demonstrating that Pnin's identity is so Russian that he is unable to comprehend a different culture. The novel does not state in so many words what it means to be "Russian" or "Western" but it does make it plain that whatever being Western actually is, Pnin is the opposite.
Bad Love
This is not a love story. In fact, it's a bad love story. The women whom Pnin has loved have not brought anything positive or fulfilling to his life: quite the opposite. Pnin tends to see his wives with rose-colored spectacles on and therefore does not see the hurt coming until it is too late, and then he is hurt and devastated. His heart is not just metaphorically broken, but anatomically broken as well due to an obscure heart condition. Pnin simply loves too hard and too much.
Social Isolation
Pnin's minimal communication skills mean that he is often isolated. This proves problematical as, to quote Barbara Streisand, "people need people". It also impacts his life over and over again in a negative way. If he had been more able to communicate socially he might have more friends or supporters on his side at the university and he might not have lost his job. There is also irony in this situation because Pnin doesn't actually realize that he is isolated, and therefore it does not cause the level of self-doubt or depression that it might in others who were able to recognize it.