Several times references are made to a photograph of the Earth as taken from space. This episode was set in October 1966. It is true that the first photograph in which the Earth can be seen is a shot taken from NASA's Lunar Orbiter 1 and published on the front page of the New York Times on August 27, 1966. However, they are not referring to the right photo. When Beth is in bed with Pete, she describes his eyes as being the same color blue as the Earth and that the Earth looks like an isolated tiny ball. The 1966 photo was black and white. Color photographs of the Earth weren't available until taken by the DODGE satellite in September 1967, so Beth could not have made the color comparison. From the verbal descriptions, they are clearly describing the iconic photo "Earthrise" which was taken from the Apollo 8 spacecraft on December 24, 1968 - two years later.
Pete asks Beth to meet him at the Hotel Pennsylvania. The Hotel Pennsylvania (the hotel's original name) operated as The Statler Hilton during this time. It was not until 1992, after several change-of-hands, that the hotel was renamed to its original name, Hotel Pennsylvania.