Goofs

Lunar module is shown being removed from Saturn V as they prepare for lunar orbit. This step would take place shortly after leaving earth orbit.

When re-docking with the command module, the lunar module is shown docking with the engine side towards the command module instead of the docking side. The LEM is backwards.

When the flies are congratulating themselves for being on the Moon, they are floating in the air, yet they should be falling or flapping their wings to keep themselves air-born. The LEM just landed and the Moon's gravity should be present.

All three Apollo 11 astronauts are referred to by the title "Commander". Any space mission only has a single commanding officer (the Command Pilot), which for Apollo 11 was Armstrong.

The antenna sticks into the LM Lunar module when they are docking.

At 1:05:25, Yegor flies into an opening in the console to sabotage the equipment. The door to the opening reads "Authorized Personal ONLY". However, this is grammatically incorrect; it should read "Authorized Personnel ONLY"

At 1:16:00, a tag on a key is seen marked "CTRL OVERIDE". Override is spelled wrong - there should be two R's.

Characters give each other "high-fives" years before the gesture was popularized.

The Command Module "Columbia" landed in the Pacific Ocean, not in Florida.

Armstrong reports to Mission Control that The Eagle will be landing off-course a few miles south of the Sea of Tranquility. The Eagle actually did land at the Sea of Tranquility, but, for the purposes of the story, it is entirely plausible that Armstrong and Aldrin were too distracted by their uninvited guests to right their course.

Amos tells Nat about the time he went on Amelia Earhart's transatlantic flight, mentioning that she landed in France. Amelia actually landed in Ireland, not France. However, this mistake could have been intentionally made to show that Amos's memory of the flight is poor.