To what extent did the three-world order not exist by 1975? What architecture of power was replacing it?

The three-world order was the world model designated as the organizing principe after World War II. The First World referred to the group of nation-states with strong capitalistic markets such as the United States, western European states, and Australia. The Second World was primarily the Soviet Union, with territory spanning from eastern Europe to Asia, but it also include. The Third World was the rest of the globe, including the most of Africa, South America, and south/southeast Asia.
Again, this was the notional organization of the globe, and it was not without inherent tensions. The biggest challenges to this order were the internal tensions. In the United States, opposition to the Vietnam War, rampant racism in response to the civil rights movement, and the assassination of President Kennedy (following an equally disconcerting period of political unrest in Cuba) made the stability of the United States as a first-world power questionable.
In South America, many countries were run by military regimes, which were quite different from the small, neutral states that newly independent countries were assumed to be. Military dictatorships like those in Cuba and the Dominican Republic threatened the already meta-stable three-world order system. Furthermore, Cuba's alliance with the Soviet Union and the nuclear weapons it held undermined the idea that Cuba was really a "Third World" country and thus questioned the merit of dividing of the globe into three Worlds. Ultimately, the idea of a neutral country was a ruse—the Soviets eagerly backed communist insurgency programs, and military dictators were eager to attain power for themselves by any means necessary.
The Soviet Union had its own tensions. After Stalin died in 1953, Khrushchev maligned much of his inhumane treatment of Soviet citizens and sought to restore humanitarianism to the communist regime. Mao Zedong, leader of the other major communist country, the People's Republic of China, executed a program called the Great Leap Forward in an effort to increase China's industrial output, and many died in the experiment.
The architecture that was replacing that of the three-world orders is a matter of debate, but this period saw the rise of the nation-state (especially after a rapid period of decolonization of Africa and Asia). Additionally, many oil-producing companies were in the "third world" category, strictly speaking, and these nations coalesced into the Organization of Petroleum Exporting Countries (OPEC) in an effort to gain more political and economic clout. It might be argued that this period saw an increase in the fortunes of oil-producing nations as well as a new liberalism in America (manifest in the civil rights and feminist movements).