How does the first part “The Ugly American” shed light on the nature of the so-called Cold War?

The first part of The Ugly American ably sets the tone for the rest of the book. In the first chapter, we're introduced to the less than impressive figure of Louis "Lucky" Sears, a has-been politician who winds up as United States Ambassador to the fictional Southeast Asian country of Sarkhan. Sears is an example of the "Ugly American" in action. He doesn't know the first thing about diplomacy, he doesn't speak (or care to learn) the local language, and he harbors racial prejudice towards the Sarkhan, whom he refers to contemptuously as "damned little monkeys."
In sharp contrast, the Soviet Ambassador Krupitzyn is a career diplomat. Both he and his wife have immersed themselves in Sakhanese culture over many years and speak the language fluently. Due to his professional training, Krupitzyn also has a much deeper, broader, more nuanced understanding of existing political realities which gives him a distinct edge over his American counterpart.
In the figure of these two leading characters, the authors of The Ugly American are making wider points relating to the overall conduct of the Cold War, particularly in the Southeast Asian theater of operations. Both the United States and the USSR are anxious to secure the support of the Sarkhanese government for strategic reasons. Yet the Americans have hampered themselves from the outset by not making the effort to step into the shoes of the Sarkhanese. They adopt an aloof, colonialist attitude to the indigenous population, making it all the more difficult to obtain the cooperation of the Sarkhanese government.
The approach of the United States to the Cold War is one of gentlemen amateurs. Contrast this with the Russians, who are thoroughly professional and have a greater understanding of what's at stake and how to go about building the alliances that will ultimately determine which side will prevail. Yes, the Russians are as self-interested as the Americans, but they understand the necessity of putting aside all prejudices and preconceptions to do what's necessary to win.
The Ugly American is not so much anti-Cold War as being highly critical of how the Americans conduct that war. The book is a clarion call for the American political and diplomatic establishment to up their game; to rid themselves of the arrogant complacency which they so often display towards potential allies and recognize that if they're not prepared to put in the effort to cultivate alliances then the Russians certainly will be.