In this series, the "White Room" - the small room attached to the Apollo landing gantry, which the crewmembers pass through on their way into the capsule - is the real thing. It was discovered in a forgotten NASA storage room, taken out and used in filming.
In episode 5, "Spider", when Astronaut Rusty Schweickart is shown entering the LM for the first time while in space, the shot has been reversed. The NASA patch on his space suit is shown in reverse and on the wrong side.
When Neil Armstrong and Buzz Aldrin walk on the moon, Aldrin says, "Magnificent desolation," and Armstrong says, "Magnificent sight out here." These lines are historically accurate, but they were actually said in the opposite order.
President John F. Kennedy: We choose to go to the Moon. We choose to go to the Moon. We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard.
President Lyndon Johnson: A great leader is dead. A great nation must move on. And as we bow our heads in submission to divine providence, let us thank God for the years that He gave us inspiration, through His servant, John F. Kennedy.