These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Wishful Projection: Seeing that most of the film is from his point of view, Takaki might not have actually seen Akari at the end of the film and it could have been a figment of his imagination due to him never being able to move past being separated from her and not knowing how to cope with it in a proper, healthy way - at least not until the very end where it is implied that he realizes that he needs to do those things, to grow up, and to come to terms with his past.
Not to mention, she did disappear a little too quick (N.B. this is probably Shinkai's most realistic film, after all). Although yes, she would be a good distance away from the railway tracks once the train has passed, Takaki would still be able to see her walking from where he is standing. Plus, trains that carry passengers go by much faster than cargo trains which would give Takaki enough time to be able to see her walking away once the train's passed, IF she actually was there.