At the beginning of the series, the Galactica arrives at Earth in the year 1980. It is said by Adama that their voyage has taken 30 years which means that the events of Battlestar Galactica (1978) took place around 1950 in Earth time. However, at the very end of the original series (in the episode "The Hand of God"), the Galactica receives a television transmission that shows the 1969 Apollo moon landing. Since the fleet's journey to Earth had only started a few months prior, it means that the events of Battlestar Galactica (1978) must have taken place at least in the late 1960s Earth time. In fact it would be at least in the 1970s since television signals travel at the speed of light and the Galactica was obviously far more than a light year away from Earth at the time they received the transmission.
In this series, no appearances are made by the Council of Twelve, despite being mentioned, and Adama seems subservient to Dr. Zee, a child prodigy under 15 years old and born after the events of the first series.