If the moon were in fact composed largely of heavy metals like uranium, scientists would have already determined this by measurements of the moon's density, which is easily measurable from Earth. An incorrect density measurement would have meant that our figure for the moon's mass would be severely mistaken, and spacecrafts attempting operations near the moon would fail to enter orbit properly.
When the Perseus enters the fracture on the moon, it comes to a stop and begins hovering with no visible means of propulsion. In order to stay aloft, the shuttle would need to constantly fire rocket exhaust downwards towards the moon.
On two occasions, Perseus collides with large meteoric debris. Considering the relative velocities of the debris and the spacecraft, both of these collisions should have been sufficient to fatally damage the craft by themselves.
The crew of Shuttle Perseus are seen walking about the cabin regularly, as if on Earth. However, in all these scenes, they are either in orbit, accelerating by rocket, or inexplicably hovering over the moon. In all these situations, Earth-like gravity would not exist.
Much of the plot of the movie hinges on the generation of a "magnetic charge." Magnetic charge only exists if magnetic monopoles exist, which has yet to be demonstrated experimentally. In any case, current theory about magnetic monopoles and magnetic charge is not reflected at all in the movie.
Space flight command rooms do not rely on municipal sources for power. They have multiply redundant independent generators to prevent the kinds of power outages that occur several times in the film. This also goes for the communications equipment.
In one scene, two fighter jets are sent up to investigate and intercept what turns out to be a piece of meteoric debris falling to Earth. Such an object would be moving so quickly, that jets would not have had time to scramble before it impacted the ground, let alone intercept and the follow it before firing a missile at it.
Technicians at the satellite control center speak as if they will fly the probe through a debris field in real time. In actuality the time it takes for a signal to get from a probe in lunar orbit that shows what is in the way added to the earth and then for earth to send a signal back to the probe and then for the probe to show that it is doing the maneuver would make such control impossible. It takes 1.3 seconds for a signal to get from the earth to the moon.
When performing evasive maneuvers, the shuttle Perseus uses its main engines (at the rear), then flies as if the wings were providing lift. To move the shuttle in space in any direction other than forward is done using the thrusters located on various surfaces.
Whenever the shuttle has to maneuver, such as when avoiding the asteroids, you can clearly hear the sound of turbine engines. Of course, in the vacuum of space, turbine engines wouldn't function at all.
There are scenes showing the Shuttle with its main rocket engines firing after the External Tank has been jettisoned. As the Shuttle orbiters do not hold any on-board fuel for the main engines - that is what the External Tank is for - these engines cannot be used once the tank has been jettisoned.
All countdowns are always to launch, not engine ignition as shown. The delay is especially noticeable with space shuttles, as main engines must start several seconds before launch to be at full power before the solid rocket boosters can be ignited.
Asteroids smaller than the one shown colliding with the moon have been detected and are already being tracked. Thus the entire basic premise for this movie - an unanticipated asteroid impact on the moon - could never happen as depicted.
The "ignition module" that John is pulling out from the shuttle's circuits is in fact the circuit board of a standard ATX computer power supply adapter (a low quality and quite old one), complete with its ATX, P4 and 4 pin connectors that are clearly visible. Anyone who opened the case of a PC can recognize it.
When Redding goes back into the building to reset a charge that went off prematurely, the dynamite charge for all of the pillars is shown to be simply attached to the sides. Real demolitions would have single sticks of explosive that would be inserted into bore holes in the pillars to be taken out. Having the charges attached to the side would produce very ineffective and unpredictable results.
When trying to stop the explosions from bringing down the building early in the movie, all that is necessary is to unplug the control wires. The detonator controls on each explosive pack are pure fiction.
When showing the Shuttle Control Center at one point, a small sign identifies the Navigation area, but the computer screen right below the sign only has a map of the United States showing on it, instead of the Moon or the Earth and Moon.
The goof item below may give away important plot points.
The only way the shuttle could get to the moon in time was using the experimental atomic rockets. Once there, ground control finally figured out that they didn't have enough power to save the moon unless they used the very same atomic rockets to boost the power of the explosion. They dutifully ejected the rockets into the crack on the moon. Without the rockets for the return trip, the shuttle would take too long to return to earth. The crew's supplies of oxygen, food and water would most likely run out.