Ordering the rocket ship to turn around, the pilot is told to make a "quick 360" turn. In fact, a 360 turn would simply turn the ship completely around in a circle to resume its present course.
Whenever people talk on the radio between the earth and the moon, there is no time lag. In reality it takes about 1.5 seconds for a radio transmission to travel one-way between the earth and the moon, and so their radio conversations should experience a 3-second lag.
When the crew are flying in the space ship, they should be weightless. But they appear to experience normal earth gravity for the whole trip.
The moon's gravity is less than 1/5th of that of earth, so walking on the moon requires a totally different stride. But in the movie, everyone walks on the moon with a normal earth stride.
In the space ship, the crew (aside from the pilot) sit in ordinary 1950's style swivel office chairs, with no headrests. In reality, these would be useless for space travel.
Retik says the air on the moon has become very thin, and the moon men wear pressurized suits with oxygen tanks when they go outside. But when Cody and Ted go outside, they do not use pressurized suits, and although they wear helmets, they have no apparent oxygen supply.
In part 6, while Cody and Ted are in a car chase, in a brief shot the back projection is going in the wrong direction, making it look like their car is speeding backwards.
Scenes on the Moon show clouds, trees and shrubs, snow on distant mountains, and occasional bird flying by.
When Cody is flying in his secret flying suit, in the long shots his arms are always stretched straight forward; but in the close-ups his arms are always bent somewhat downward.
Near the end of Chapter: 10, during the gun battle you hear the sound of breaking glass as gun shots are fired, but no windows break. The windows are closed and Cody and Graber are shooting through closed windows at each other.
During fist fights with Commander Cody he often reacts to the punch, as though he was hit in the face. But he wears a helmet. And the guys he fights with never hurt their fists from hitting his helmet.
In Chapter 1, when Cody wins the shootout with Graber and Daly, they decide to flee on foot. There is no reason for this; if they had taken the truck, they could have gone faster than on foot.
There seems to be no reason for Joan to come on the moon flights: she doesn't do anything.