France had major disagreements with the rest of NATO. They never fully left NATO, but they did remove French forces from the integrated command structure of NATO, only allowed French-NATO troops to be stationed in France, and banned foreign nuclear weapons from being housed in France (They of course kept their own).

The Sino-Soviet Split was an important division between the USSR and Maoist China, starting as a doctrinal dispute over the legacy of Stalin with the revelations of Khrushchev's Secret Speech of 25th February 1956. With Khrushchev denouncing the 'Cult of Personality' of the Stalinist version of Communism, Mao took this as a personal attack on his leadership style, and in fact temporarily lost his dominant position in the CCP. This doctrinal difference, combined with tensions over the Soviet expectation that China should be the 'junior partner' in the Communist camp rather than an equal meant that by 1960 relations between the two nations were extremely poor, and through most of the 60s and 70s until the death of Mao they would remain so, only recovering slowly, and never fully, throughout the 1980s.

The tensions between the two countries were so bad that throughout 1968-9 there were repeated skirmishes between the troops of the two nations on their mutual border and there were somewhere in the region of 250,000 Soviet troops, and a greater but unknown number of Chinese PLA troops facing them.

These tensions also extended into proxy conflicts, in a similar vein to the US and USSR, with China sponsoring opposing groups to those sponsored by the Soviets (notably supporting Albania after it continued upon a Stalinist model after 1956). It also gave training an support to the guerillas in Afghanistan during the Soviet intervention of the 1980s.

Within Europe, there was the separation of the Yugoslav communists from Moscow in 1948, which was a legacy of the Second World War. Tito and his guerillas had required no support from Soviet forces in liberating his country and was genuinely popular in a way that no other communist party was in the aftermath of WW2. After 1947 there were increasing calls to implement 'Stalinization' in Eastern Europe from Moscow, which involved among many factors, the final suppression or absorption of non-communist socialist parties, destruction of all social organisations remaining outside of communist control, and moves towards crash collectivisation of agriculture. Tito and other communist party members in other nations disagreed with aspects of the implementation or timing of this initiative, but Tito was the only one strong enough, and with a secure enough powerbase to resist Moscow, but was isolated from the other Eastern European nations as a result (many other leaders who resisted such as Gomulka in Poland were expelled from the Party and served long prison sentences or were executed)

After the death of Stalin, as noted above, Albania rejected destalinization, and was isolated from the other communist nations, with the exception of China increasingly from 1958. This isolation and lack of natural resources contributed to it becoming the poorest and least advanced nation in Europe through to the present day.

Finally Romania under Ceaușescu (1965-1989) strained against the limits of its place in the Warsaw pact. After the examples of Hungary and Czechoslovakia, it never openly defied its obligations either to military contributions, or socialist principles, but it sought to maintain better, and even independent relations with Western nations at odds with the general trends of Soviet sponsored socialism.

Sources: 'Comrades' by Robert Service 'Two Suns in the Heavens: The Sino-Soviet Struggle for Supremacy 1962-7' by Sergey Radchenko 'The Rise and Fall of Communism' by Archie Brown