Goofs

44:15-44:33 into the run-time, during the border-crossing, the Spanish broadcast [via English subtitles] says: "the American spacecraft known as the Eagle is on course toward the lunar surface. The spacecraft carrying Neil Armstrong and Buzz Aldrin is now now [sic] flying on its own power. It should start its descent in approximately one hour." If they had only said that it was on its own power, it would not seem so egregious in the next scene (and several minutes later) for the Eagle to still be docked to Columbia as they could be connected but now "on its own power", however the announcer first said "on course toward the lunar surface".

Although some of the Apollo astronauts did race their Corvettes, they did this mainly in Florida on the Cape Canaveral runway. Stories of them street racing are apocryphal.

Deke Slayton is depicted as being a smoker. In reality he quit smoking in 1962 as part of his effort to get rid of the heart fibrillation that had prevented him from going to space.

When Gordo Stevens rushes home to see the Moon landing on TV, his wife says there's "no video" yet. People in 1969 wouldn't use this word, as it came around in the 1980s and gained currency in the Internet era. She would've said there's no picture yet.

While home video only became widely popular in the 1980s with the decrease in price of VCRs, the term "video", and the technology behind it, had been in existence since the earliest days of television.

One engineer tells another to "stay in your lane." This idiom only fell into popular use in the 2010s, and definitely would not have been used in the 1960s.

The song "Put a Lid On It" plays over Margo quickly dressing. Unlike the other songs in the series, which are correct to the period or pre-date it, this is a swing revival song written and recorded in 1996, not during the original swing era.

When crossing border illegally, the Mexican guide tells the group about a crossing "half a mile" in a certain direction. He should be using kilometers, as imperial units are not commonly used outside United States and Britain.