Paranoia Fuel: If you live where a major earthquake is expected, this could very well cause some mental discomfort.
Shocking Swerve: Mirai's descent into apparent hallucinations after Yuuki's sudden death was not particularly well-received by a portion of the viewership, as it marked a shift in tone from objective and realistic to either supernatural or subjective (Mirai's POV). Yuuki's death itself also appears to be a case of this at first; had Yuuki suffered a cerebral hemorrhage as suggested by fans, however, his condition would likely have deteriorated that quickly.
Some Anvils Need to Be Dropped: While disasters are definitely scary situations to be in, popular culture's depiction of disasters is exaggerated for entertainment and is not always accurate of real life. You'll be okay as long as you stay with people you can trust (most of them feel Not So Different from you!), follow directions given by government officials & the news (and if you can, try to apply what your school has taught you in emergency drills), and you can't blame yourself for things that happen outside of your control.
What an Idiot: Kento risks his life to save a mass-produced reconnaissance robot.
Woolseyism: In the Japanese version, Yuuki and Itsuki call Mirai the phone alien. The English dub tweaks it around to make it sound more alien-like, having them refer to her as the "Cell phonian," which is much more creative and sounds just like something a seven or eight year old kid would come up with. It's the same thing with "Frogworlder" and "Sergeant Snack Time."