An interesting irony of the movie Don't Look Up is that, while it is very good at understanding the media and manipulating public opinion, it is profoundly unconcerned with showing an accurate portrayal of the physical world, and it knows that its audience is equally unconcerned.
They might have done this intentionally, as a meta-level joke, or they might be assuming that the audience would consider these acceptable breaks from reality in a metaphorical or allegorical tale, or they might simply be ignorant. Either way, in order to have that discussion, you have to at least notice the inaccuracies. If you were not aware of these, i.e if your brain just ignored the lies someone was telling you because they were embedded in a narrative that validates your political beliefs, then you're part of the problem.
Here is a partial and incomplete list of some of the more obvious and egregious scientific blunders, roughly in the order that they appear. I am not an astronomer or physicist, I am just someone who knows a few basic facts about science (spoilers, obviously, although this is the kind of movie where they really do not matter):
1) It's standard practice among observatories to confirm sightings with lots of other observatories before going public or informing any authorities. It is extremely unlikely that a single team would bear the responsibility of informing the world, it would be a worldwide collective press release from all the observatories.
2) All of the nukes in the world would not be enough to meaningfully change the trajectory of a 6 km, hard, dense, rocky object a few months from impacting Earth. NASA does not have any contingency plans for an object of that size and approach.
3) Nobody ever launches that many rockets simultaneously from the same site. They would go up from different locations, or be launched in sequence to rendezvous in orbit.
4) I don't care how many rare earth metals are on that thing, there's no way it's worth more than the world's annual GDP. A large increase in available quantity would quickly drive the per-unit price down to almost nothing.
4a) Rare earth metals are not some magic crystal that makes wealth. They are like spices in a recipe. Yes it sucks if you run out of turmeric, but someone delivering a metric ton of the stuff to your kitchen will not give you any more actual food, or increase your ability to make it.
5) Rare earth metals aren't actually that rare, they're just a bit expensive to collect and refine. Retrieving them from an impact crater at the bottom of the Pacific Ocean would be vastly more expensive than opening up existing reserves that people aren't bothering with right now.
6) Breaking up the object and allowing each piece to hit the planet would do about as much damage as the whole thing hitting at once.
7) There's no possible way that you could see the comet while driving a car on a main street in a town. You can barely see any stars under streetlights because of the light pollution.
8) Russia is much more competent than that at launching nukes into space. So is China for that matter, and there's no reason they would need to do a single joint launch. They'd each launch things up separately and coordinate the impacts after they were in space.
9) Even if the Russian mission failed, it would not have failed in a nuclear fireball. Nuclear missiles don't work like that. They are specifically designed to not blow up accidentally in case of a launch vehicle misfire. They stay disarmed until you tell them to arm.
10) Big data analytics does not work that way. Just no. Not even a hypothetical super-intelligent AI could have accurately predicted the president's fate with the information available at that time.
11) A black man would probably have his own family to be with, rather than being a white man's lifestyle accessory.
12) Our civilization does not have the ability to put people in cryo-sleep, nor could we make a fully automated interstellar colony ship. These things are many decades away, not something a tech billionaire could have hidden away in a lab.
13) Objects blown into space by a planetary impact would no longer be recognizable.
14) The post-credit sequence basically invalidates the entire movie. If someone is capable of crawling out of the rubble of a NASA command center, which to be clear is not a hardened bunker like Cheyenne Mountain, and finding an atmosphere with breathable air and livable temperature, then millions of people could easily have survived the impact with a bit of prepping.