Factual error: When they are in quarantine after returning to Earth, they are in a room with several magazines. One of the magazines is an issue of National Geographic with the cover image of them standing on the moon. That is the December 1969 issue of National Geographic, whereas they were actually in quarantine in late July/early August 1969.
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.
Factual error: As depicted in the film, the lunar lander touches down and settles onto the surface of the moon (as shown by the shaking of the landscape stopping). Buzz then reports a "contact light" and Neil orders the engines turned off. In reality, three of the LEM's legs had probes extended for a couple of feet below them, and the contact light would activate when one of the probes touched the surface. This meant the ship was still several feet from touchdown, so the astronauts would turn off the engine and let the moon's gravity complete the landing cycle. So either the film's depiction of the contact light being called would be several seconds too late, or the actual touchdown is depicted as being too early. Take your pick.Vader47000
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.Vader47000
Factual error: The Apollo 11's stage separation is depicted incorrectly from the onboard view. It shows the interstage falling away, which was done for the last time on Apollo 6, whose footage is often mis-represented as being from Apollo 11, which did not have the onboard film. Also this separation in First Man is the first stage separation, shown by the multiple nozzles of the second stage, but is depicted as being immediately before trans-lunar injection, which would in fact be the second stage separation.