These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
That would be David Arnold, who went on to score both Brosnan and Craig era James Bond films.
Harsher in Hindsight: Thanks to the now disturbing images of the destruction of the Empire State Building and the White House, this movie wasn't aired for a long time after 9/11. But since 2009, it came back on TV.
Particular the image of the shadow crossing over the Twin Towers.
And the wall of fire spreading through the streets of NYC, much like the wall of dust produced by the collapsing twin towers.
When the aliens first arrive, one spectator says "Oh, I hope they bring back Elvis!", and later, after escaping the mothership, Will Smith shouts "Elvis has left the building!". In his next movie, Men In Black, he asks "You do know Elvis is dead, right?", to which he's told "No, Elvis is not dead, he just went home.".
Adam Baldwin has a supporting role and Raphael Sbarge makes a very brief appearance in the film. Over a decade later they would both become involved with a popular video game franchise also involving an invading alien race decimating humanity, has destroyed several other races in the past, and has forced multiple factions to unite against them.
Inferred Holocaust: With most of the world's major population centers blown up and massive chunks of alien debris crushing landmasses and plunging into the ocean (no doubt creating tidal waves), the world does not look positive in the wake of the attack. Then again, since the alternative was total annihilation, there's only so much room to complain.
"Today, we celebrate our Independence Day!" Really, that whole speech entered pop culture and hung on for dear life.
Money Making Shot: The alien ship blasting the White House is the emblematic shot of the movie. After that, it's the shadows falling over major landmarks, and their destruction that was the basis of the trailers.
Moral Event Horizon: The aliens' blowing up several cities at once is terrible, but what truly cements the aliens' status as unforgivable, especially in-universe, is when the captive alien reveals that they want to annihilate humanity, and they have done this to countless other worlds in order to steal their resources. Simply put, they're planet looters!
Snark Bait: Despite how much of a financial success this film was (with a worldwide gross of $816,969,268, the second-highest gross for a movie of all time back when it was released), the film attracts plenty of snarkers - especially non-American snarkers, who typically don't take kindly to America Saving The Day.
Like most blatantly pro-American movies, this results in picking apart the movie on every conceivable level, essentially demanding a higher standard than any other movie would be subjected to in terms of accuracy, depiction of other countries, and plot. For an example... well, just click back over to the main page and see the sheer number of nitpicks.
After Hiller parachutes from his jet, it's clear that "he" is just a dummy tied to a parachute when it collapses in a heap on the ground, followed by a cut to Smith recovering.
Strawman Has a Point: Nimziki gets two. We're supposed to be against his suggestion of using nuclear weapons but considering what we've seen so far that would be closest thing to a reasonable chance of success. Later he's supposed to be showing incompetence and cowardice for being against the plan to infect the mothership but the plan relies on a lot of luck, a human pilot managing to use an alien vessel, the aliens not getting suspicious and if it failed it would probably mean the end of all organized human resistance.
Toy Ship: The President's daughter and Hiller's stepson
Visual Effects of Awesome: It still holds up well and the scope of the movie is awe inspiring. The sense of size and scale has not been matched by any movie since.
A lot of why it holds up is that most of the effects were practical effects and models, with just a bit of CGI for laser blasts and other things that don't have to look "real" to fool the eye. Shortly after this came out these techniques were largely abandoned in favor of all-CGI effects, which the viewer's mind automatically flags as animation.
What an Idiot: Tiffany, who ignores Jasmine's warnings of getting out of town and instead heads directly to one of the gatherings directly under one of the alien ships. Guess what happens?
Albert Nimzicki is the Secretary of Defense and an entire fleet of alien spaceships shows up and float ominously over the world's major cities. As the former head of the CIA (it's stated somewhere in the movie that Nimzicki was this), he becomes privy to the fact that Area51 has indeed been housing a crashed flying saucer and alien corpses and been studying them and their tech for decades. Does he choose to immediately inform the President about everything the research had discovered in order to better inform his decision-making? Nope.
Debatable; while he makes (in retrospect) bad choices, his working assumption that launching nuclear weapons will defeat the invaders remain untested for long, and it isn't exactly unreasonable (at least before the first counterstrike with fighter planes fails) that it could work. If nuclear wepons would've worked, there would be no need to reveal Area51.
Woolseyism: Will Smith's "Elvis has left the building!" was changed to "Last train to Mikkeli has just left!" in the Finnish DVD.