Trivia: The scene where Will Smith climbs aboard the crashed craft ("Welcome to Earth") was accomplished by using forced perspective, an in-camera technique that is as old as cinema. The ship is much closer to the camera than Will is, but it gives the illusion he is climbing aboard this massive craft. The technique is also used elsewhere in the film but this is one of the best examples.
Trivia: Spoilers: When Russell sacrifices himself and drives his plane into the laser, pay attention to the laser exploding in the first shot. It's actually cleverly reused footage of the Empire State Building exploding from the initial attack scene earlier in the film. The image has just been flipped vertically and augmented with some extra fire/explosions to mask the details of the building. But if you look very closely, you can totally tell.
Answer: Remember that the aliens had to interface with our satellite computer code first...David simply "reverse engineered" the code to create the virus. When it was uploaded, they didn't have enough time to combat it.