In Adrian Mallory's drinking scene started at 16:50, the old forester bottle is rotated at 16:53 to the wrong angle, then back again during following scenes.
Buzz Aldrin has stated that the flag they left on the moon on Apollo 11 mission was knocked over when they blasted away from the surface with Lunar Module. Still several times during the episode they show footage of it standing upright until its knocked over by the Chinese with their lunar rover. The flag is also bleached by the radiation and would now appear white.