The sensation that I've lost something lingers.
The movie begins with both of the two main protagonist looking up at the sky with a feeling of something missing from their lives. The sense of loss is present in them, and they are wandering about trying to remember. This introduction to the movie is repeated at its end where they finally meet again as adults. It represents their fate, their fated love story and how it comes to a full circle at the end, with the story of their meeting in the middle.
Braided threads are the god's art and represent the flow if time itself.
The tradition and religious beliefs are deeply integrated into the story. Mitsuha's grandmother and her persistence on taking care of the shrine and insisting on her granddaughters keeping up with it, shows the importance of it and the huge part it plays in the story and the change of time that saves the people of Itamari. The movie shows Hitoha and granddaughters twisting and knotting the threads several time throughout the movie.
Wherever you are in the world, I will search for you.
Taki and Mitsuha meet at Kataware-Doki, at twilight, when there exists a possibility to meet someone from the other world. They meet each other at different timelines, each return to their body, and make promises to find each other again, no matter where they are in the world. A promise they actually keep at the end, after the disaster got prevented.