Brainerd swings the laser wide twice while trying to cut through the surface of the moonstone. Had it been a real laser, he would have burned holes in the bulkheads of the lunar station.
At 7:26, while on the lunar surface, Major Anderson stumbles down a ramp that makes loud metallic noises. He also audibly hits hard the floor of the set. The moon's atmosphere is a near vacuum, so these sounds could not have been transmitted. He would also have weighed a good deal less, which would make his fall a soft landing.
In the final act, when General Stocker and Major Anderson begin walking back to the outpost after leaving the moonstone on the lunar surface, they clearly cast multiple shadows in all directions on the ground. This would be impossible, as the only light source - the sun - would be radiating from only one direction.
Gen. Stocker decides to send the moonstone to Earth to prevent its capture by the Grippian warship. The Grippians inside the moonstone had already told him they would die immediately if they were sent to Earth.
Prof. Diana Brice agrees to marry Gen. Lee Stocker but then can't go along with it after hearing only Major Clint Anderson's scant account of a past event (a one-sided account), never hearing Major Clint Anderson's side - the man she supposedly loves.
The alien refugees prevent Major Anderson's death but insist no one touch him. Why? At the end of the scene, Prof. Brice touches him but now it's not a problem at all.
The refugees don't want their powerful accumulation of knowledge to fall into the hands of the tyrants from Grippia, yet they readily engage in passing their advanced knowledge to Earthlings. Who's to say the tyrants couldn't then take it from the Earthlings or that the Earthlings themselves wouldn't then become tyrants from gaining all that superior knowledge?
Major Anderson drinks openly from a flask and gets sloshed from it. The proof must be pretty high to get that drunk from one unfinished flask. He would have to have taken aboard much more alcohol than that on his moon flight, a flight in which every ounce is accounted for. If he took that much aboard, why would he need a flask to hide it or keep it handy?
Prof. Brice calls Dr. Mendl "professor."