Factual error: The interior shots of the Gemini and Apollo Spacecraft show worn and dirty panels, knobs, switches and circuit breakers. The movie most likely used some original cockpit trainers, but in reality the astronauts were flying brand new spacecraft that were spotless.
Suggested correction: All spacecraft are extensively checked out by technicians before mating to the launch vehicle. Launch rehearsals are done over and over again by both prime and backup crews in the real vehicle in the weeks leading up to launch. Gus Grissom, Ed White, and Roger Chaffee lost their lives in a fire aboard Apollo 1 during one such dress rehearsal. The switches and panels get worn from this use and activity. Crews also make minor modifications to their specific craft to suit the mission and tastes.
Factual error: When Neil Armstrong drops the bracelet into the crater he lets it drop straight down. Yet the bracelet appears to fall a long way, implying a very sheer cliff, close to 90°. This is not natural for a lunar crater, as the maximum steepness of crater wall is determined by the material's angle of repose (how steep before it avalanches) which has typically been observed to be approximately 45° for lunar regolith.
Suggested correction: "Not natural" and "typically" don't mean it's impossible. It's unlikely, perhaps, but unless it can be proven to be impossible, it can't be said to be a factual error.
"Not natural" in this sentence means not found in nature. Thus, it is impossible. Typical just means most often or, on average, but certain ranges can be impossible. If a high school does not allow students over the age of 25 to be enrolled, you could say the average age of a senior is around 17, but it could never be over 25. If you want to correct the mistake as being factually possible, you have to provide evidence or proof.
Factual error: Armstrong sees the first quarter moon through one of Columbia's windows during the launch. However, the Command Module was sheathed in a protective shell that included an escape tower in the event that the launch had to be aborted. According to Michael Collins in "Carrying the Fire", the windows were covered until the tower and shroud were jettisoned when the Saturn V reached an altitude of 60 miles. Additionally, on July 16, 1969, the moon was two days past New Moon, only 4% illuminated, and would have been too thin and too near the sun's glare (from Earth's perspective) to be seen without optical aid. It did not reach the phase depicted until July 22. Later the same day, when Columbia docks and pulls Eagle out of the second stage housing, the Earth appears just shy of a first quarter phase. In fact, the Earth was nearly full, since Earth's phases are always opposite those of the moon.
Suggested correction: Most of this comment is accurate. One quibble: the Apollo capsule was covered during launch, but the cover contained openings for the hatch window and the commander's window. In other words, Collins wouldn't have been able to see outside, but Armstrong would.
Factual error: The Apollo 11 lander Eagle detaches from command module Columbia with its landing legs already extended. Neil is then shown saying "the Eagle has wings" as if to mean the ship is flying on its own. Actually, the ship's legs wouldn't be extended until after the undocking. It was the extension of the legs that prompted Neil's quote about the Eagle having wings.
Suggested correction: The legs were, in fact, extended prior to undocking. I was comparing it to the "From the Earth to the Moon" depiction.
