The metal "freezing rod" is shown with frost on it, yet in the shots of Steve being attached to it, the rod's surface is bare.
The cable that Steve uses as an Indy-Jones-style bull-whip is not long enough to reach the merc, especially if the cord has to also be long enough to wrap around the barrel of the villain's blaster a couple times to tether it and jerk it away.
The merc who is doing the pounding of the rod through the Moon's surface is hammering very slowly and making almost imperceptible progress, yet the end of the drill rod is shown breaking through and moving down into the room very rapidly.
Various light-angles of the Earth and Moon do not "match with each other"; in other words, there is sun-lighting from different angles at once in the same shot.
Pounding a simple bare hard steel rod through the moon's crusty rocky surface and down into the mining chamber would not create a sufficient seal in the rock around the rod to prevent the pressurized air in the chamber from escaping into the moon's airless atmosphere within a few seconds, instantly killing everyone in the chamber.
Shot of radio antenna silhouetted against the sky is obvious double-exposure with superimposed rain; the shot is of a clear calm sunset scene, not an overcast rainy afternoon.
Steve says the moon's orbit is circular when it actually is elliptical. As an astronaut he would definitely know this.
The mirrored light-beam would not melt ice, especially from such a great distance and through such cold airless (non-heat-conductive) atmosphere.
Bright light comes from the side in some of the lunar surface shots, even though the scene represents the dark side of the moon.
The wires that the lead merc supposedly fuses together do not actually get melted or welded together; they are plainly unchanged after the impressive-looking blue flash and smoke subside.
The red digital readout that Bess is watching to monitor the supposed countdown to destruction is obviously not a numerical timer, since it does not count down by seconds; several seconds elapse between each change in number.
When the mercs are trying to blast through the rock with their laser guns, the electronic blast sound is not heard after every visible laser bolt.
Steve does not use the radio's push-to-talk mike during part of the time that he is altering the bomb, and he is too far away from the mike to use voice-actuation while speaking in a normal voice, so there is no way that the people on Earth could hear what he is saying to them.