Section 1 is about a variety of places that the speaker is from. He references California, Missouri, the Dakotas, and several other locations across the United States. Since the majority of Whitman's work is a search for self-identity, this appropriately demonstrates his effort to mark himself as an American, a man who represents many different aspects of our culture. In citing these different locations, he also cites the different aspects of geography: rivers, cities, and plains.
Section 6 is about giving credit to the great thinkers of the time: poets, philosophers, inventors, and politicians. It is almost as if Whitman has the speaker honoring those thoughts that have gone before so he can envoke the Muse of thought to give him a greater ability to continue with the exploration of the Soul that he intends to discuss.
Section 52 is about the speaker concluding his thoughts. He notices he has spent a great amount of time discussing his ideas. He cites his famous "barbaric yawp", that deep expression of the self in this section. He equally notes his passage in time. He realizes that he will die and one day be the dirt underneath the feet of a reader. This connects back to the first section he had related to the beginning of his life as here in section 52, he is at the end.