Patzer

When Grant spacewalks to the dead ship, we see him from different angles, but always with sunlight coming from the direction we're looking from.

When the rescue shuttle is launched, both solid rocket booster separation and main engine cutoff are called, yet the video screen in mission control shows a lunching shuttle still under power.

When Mera is woken up and Koenig's character cradles the back of her head with his space glove under her hair: next closer up shot and it's now over her hair.

The full Earth is visible from the sunlit lunar surface, which is impossible.

The scientist claims the corpse and the pod retrieved from the spaceship have been Carbon 14-dated to be 14,000 years old. But the Carbon 14 method only works for creatures/objects that lived/were created in the Earth's atmosphere.

At the end the full Moon is seen against a dusk sky, which is impossible.

(At about 1:21:00) On the lander panel, when Grant and Mera are setting the self-destruct in the alien ship, the word Auxiliary is misspelled "Auxillary".

During the start of the Intrepid shuttle from Earth, the astronauts are seen working at the shuttle controls while the launch vehicle is under full power. This is not possible due to the extreme high g loads during launch. They should have been strapped to their seats, motionless.

All of the action on the "Moon" clearly takes place in Earth's gravity, not the Moon's reduced gravity.

When Grant and Mera first approach the moon buggy, she's shown in closeup. Her neck is visible between her helmet and spacesuit for an instant, meaning the suit and helmet are not connected.

An Uzi has a maximum capacity of 32 rounds, but Jason and Ray appear to fire more than that, and never change their magazines. But when Mera fires from within the shelter, the firing rate is quite slow, so they may not have used all that many rounds (and we may not have seen them exchange clips)

After the push-up contest between "Jason" and his son in, the boom mic is visible floating above them as they talk in the kitchen.