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.
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 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.
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.
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'