Getting what you wish for
Mitsuha wishes for a different life. She wishes to the sky to be born as a handsome Tokyo boy. When her wish comes true the next day and Mitsuha wakes up in a boy's body in the middle of Tokyo, she realizes the consequences of her wish. Not only does she have to deal with embarrassment of the physical aspect, but also face the disorientation of a completely new life. It isn't all rainbows as she imagined, and filling in Taki's shoes isn't all that easy.
Townsmen of Itamari not wanting to listen
Taki in Mitsuha's body devises a plan to prevent the disaster of the comet that is about to take many lives. It turns out to be not that easy to convince the townsmen of their impending death. They refuse to listen, calling Mitsuha and her friends crazy, not wanting to believe that something like that could ever happen.
The comet
The news of the comet passing by are exciting and all the people can't wait to get out to look up into the sky. It is ironic that such a beautiful event could bring so much misery and death suddenly and without anyone imagining it could ever happen. The comet suddenly splits and a small portion of it falls on Itamari, letting a disaster ensue.
Unhappy with what you have
Mitsuha is clearly unhappy in Itamari and wants to leave. Itamari is an idyllic little town that could represent the heaven for some, but Mitsuha doesn't see it that way. Neither does Taki feel completely content with his life in Tokyo, a dream for Mitsuha, and seems ironically really happy in Itamari, even being able to draw it from memory. It seems that by dreaming of something different, the characters don't see what they already have, which could universally be seen as the curse of mankind.