In the first part, a series of delays from inclement weather cause Takaki to slip further and further past his intended meeting time with Akari, with at one point an explicit 2-hour delay. This causes him to express the concern and hope that she actually went home rather than staying out waiting for him. When he finally reaches Iwafune station, he discovers that she waited for him at the station after all.
The very end, where Takaki may have finally found Akari again.
The movie is basically an hour-long parade of CMOH and Tear Jerker moments.
Do you know why Takaki smiles at the very end? It's because he was able to see the cherry blossoms with Akari again.