The majority of the story takes place prior to December 1965. At one point, one character asks another character if she has seen the movie "Doctor Zhivago." That would have been impossible, however, since DZ would not be released until the final week of December of that year.
Gus Grissom is shown with a silver 1960 Corvette. Gus Grissom had a 1967 Corvette when he died so the 1960 is incorrect for this episode. As Jim Rathmann and Chevrolet were supplying the astronauts with Chevrolets through a special lease deal starting in 1962, rumored to be something like $1 per year for two Chevrolets, the idea of an astronaut driving an old Corvette doesn't make sense. The Grissoms driving a 1960 Chevrolet station wagon also would not make sense, as it would be five years old at the beginning and almost 7 years old at the end. At this time, most people only kept a car two years before trading it, so the Shepards should have been in at least a 1963 as some of this story is in late 1965.
Gus Grissom's silver 1960 Corvette is shown in the drive as he leaves to go test the Apollo but he actually owned a red 1967 427 Corvette convertible at this point in time. He had also had a white 1964 Corvette convertible and a black 1965 coupe, which were not shown in this series.