When in Margo Madison's office with Deke, Buzz, and the NASA director, Deke is in a flight suit with a name patch showing Naval Aviator wings. Deke was in the Air Force, though.
This episode treats the question of whether to relay the information to Ed about his son's accident as if it is unprecedented. While some details of the story are unique (Ed is stranded on the moon), similar scenarios have been encountered in the past in other government agencies (e.g. with soldiers or intelligence agents working in classified, compartmentalized operations). NASA operations would know this.
The Stevens' Christmas Tree appears to use LED lights. In 1974, it would have used incandescent bulbs.
Early in the episode Karen Baldwin learns that her son, Shane, was struck by a hit-and-run driver. Yet, she is never interviewed by the police nor is there any indication that this incident is being treated as a crime.