Far be it from me to critique Independence Day in terms of accuracy, but I do have one quibble right from the start. As the alien mothership approaches Earth, passing over the Apollo 11 landing site we see the Star Spangled Banner.
Problem: our flag is not still there1.
Or, more precisely, it's not still standing (sorry, Rocket Man). See, it's hard to plant anything on the moon because its dust ain't like dust down here:
The regolith...is formed by a sort of fine dust, but it's extremely sticky. It's curious to note, that it takes quite some efforts to plant the American flag in this material, an observation often contested by Moon landing conspiracists. On Earth, dust, formed by weathering of rocks, shows under the microscope tiny grains with smooth edges. Moon dust is formed by tiny fragments of rock with sharp edges. The edges of the single grains tend to get caught into each other, like in a sort of zipper.
Yeah, nobody had anticipated this:
[Armstrong] and Aldrin unfurled an American flag, stiffened with wire so that it would fly on an airless world, and struggled to plant it in the dust. As hard as they tried they could push the flagpole only six or eight inches into the ground. For a moment it seemed the flag would fall over in front of the worldwide audience, but at last the men managed to steady it; then they backed away.
So when they left (watch what the ascent engine did to Old Glory):
“We’re off,” Aldrin exulted. “Look at that stuff go all over the place.” Outside, a spray of gold foil and debris from the descent stage flew away in all directions. The flag toppled to the dust.
And that was a good learning experience, even if we littered.
In conclusion2: They could send a man to the moon, but they couldn't think to place the flag away from a rocket so it wouldn't get blown over.
1 - Not fluttering, at least! I'll also cut them slack on the visible stars.
2 - Borrowing from Dave Foley, playing Apollo 12 LMP Al Bean.

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