While this chapter doesn't come right out and point out the whirligig, when the man gets off the boat and walks down the pier, he stops to look at the "wooden marching band." This is the whirligig that Brent made. It is true that this chapter is the least loosely connected, and it is hard to see the whirligig connection at first. But the marching band whirligig is the same one that Brent made and left on the beach in Miami.
The significance of this chapter is how this particular whirligig touched the man's life. He is looking for peace, and lives a crazy life with lot of noise and people and never a moment of quietness and rest. He doesn't have much privacy and has had some tough times. He wishes he were like a particular sea bird, one whom he imagines just quietly flies over the calm ocean, alone, without a loud, annoying, stressful family. However, when he takes a boat ride looking for this bird, he realizes the bird flies in a flock and is always with its loud, raucous family. The man gets off the boat and looks at the marching band whirligig that Brent built, and realizes basically that it takes a band to make good music. It takes more than one person to make a family. And just as the birds need their flock and a marching band needs many members, a human needs his family too. Even though things are sometimes crazy and loud and people argue, in the end they "make good music" together. He realizes the value of his family and finds another way to find peace in his life, which is to enjoy the peaceful night while he works his new job.
On the last two pages of Chapter 4, the street sweeper, who is taking a drive by himself to find peace from his family situation, comes across a little marching band made of wood nailed to a restaurant on a pier. The marching band is actually a whirligig, made by Brent and placed in Florida (see Chapter 7, "The Apprentices"). The marching band leads the street sweeper to come to an understanding and acceptance about people, and the things that happen when they live together.
As my colleague so aptly pointed out, the chronology of the story can be confusing, but as you read through and match up the chapters, it should begin to make more sense.
The book flashes forwards in a reverse chronology to stories within the story about how the whirligigs effects those who see them. Although i do not have the book in front of me, I'm sure that this is probably what is confusing you.
two trials that the narrator goes through in chapter 4