This is Barry Sullivan's second appearance in the series in the role of the unpleasant Senator Creston Collins. He was also seen in this role in "The Inquiry", an episode in Season One. Sullivan also acted in the "L.A. 2017" episode in the third series, but he had a different role.
The "Bay of Pigs" affair gave President Kennedy a major setback to his prestige soon after his inauguration in 1961. A small, armed force of exiled Cubans, after training from the CIA, was landed at the Bay of Pigs, Cuba, from American ships and made a wholly unsuccessful attempt to overthrow the revolutionary regime of Fidel Castro; the invaders were mostly either captured or killed. President Kennedy publicly took the blame for the incident, although it had been set in motion before he became the President and he was not told about it until a relatively short time beforehand. Privately, he furiously vowed to destroy the power of the CIA, although he did not succeed in this.