The large storm that is hitting Florida is seen several times during the movie, both from space and on computer monitors. Sometimes it is rotating clockwise, sometimes counter-clockwise.
During a walk-through of the control room at ASI, there is a screen shot of the shuttle crew days before the launch.
During the initial stages of the shuttle flight, the crew are shown wearing space suits and helmets, then abruptly the helmets have come off, and then right after firing the nuclear pulse boosters the crew are seen wearing blue cotton tops.
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.
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.
When the building is demolished, the charges all fire together. This is incorrect. Charges are set to explode in a specific pattern to allow gravity to pull the building down in the desired direction.
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.
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.
After the asteroid collides with the moon, the female researcher examines an important scientific document. On the document's cover page, Astronomy is incorrectly spelled "ASTRONOMEY."
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.
The blue telescope the woman is looking through in the opening sequence is aimed backwards, i.e. at the ground, not at the sky.
The scenes with the F-15's taking out the incoming asteroid (as well as the tracking data on the computer screen) are re-used from the movie 'Solar Attack' where two F-15s are scrambled to take out a falling Russian Communications Satellite. Closeup of the computer screen at 0:31:04 even says 'RS COM SAT'