Imagine growing up in the Estonian capital city, Tallinn, during the cold war and discovering “Dallas” transmitted by television from Helsinki across the Gulf of Finland. Life in the 1970s was drab in Estonia, then a Soviet republic under the thumb of Moscow.

In the eyes of the Communist leadership, that American serial with its jousting millionaires epitomized the creeping allure of capitalist decadence.

In the facetiously lighthearted documentary “Disco and Atomic War,” the director Jaak Kilmi, who grew up in Tallinn in those days, recalls how the exploits of J. R. Ewing and company mesmerized his city in the far north of the country, where the broadcast infiltrated the Iron Curtain....