The mission is referred to as "Apollo 1" throughout the episode, with the three wives showing annoyance when Deke Slayton tells them that NASA wishes to re-designate it publicly as "AS-204". In reality, the mission was never referred to as "Apollo 1"; it was the wives of the astronauts who asked that this designation be used, which was made official in April 1967, three months after the fire.
Just before the fire, Gus Grissom says "I can't hear a thing they're saying" (with annoyance) between saying "How are we going to get to the Moon if we can't talk between three buildings?" and "Jesus Christ". In actuality, Ed White said "They can't hear a thing you're sayin'" (with a smile in his voice) between Grissom's two comments.
Some 1990s cars are visible in the background in the Washington, DC scenes, although the episode is set in 1967.