It seems that watching the entire _Kimagure Orange Road_ series (TV series, OVAs, and movies) is becoming a yearly summer event for me. I've just watched the TV series for the third time, and the OVAs for the second. It's unusual for me to watch ANYTHING, anime or otherwise, more than once, so there must be something unique about _KOR_, at least for me. This first movie is one reason why.
As the other reviewers have mentioned, the basic purpose of _I Want to Return to that Day_ is resolving the romantic triangle that has persisted throughout the 48-episode TV series and the 8-episode OVA one. But it also shows the characters realizing they're outgrowing their high school sensibilities and, well, moving on. Remember how you hung out with a group of friends through high school? How you started to drift apart as graduation approached and you all decided to go to different colleges? How things simply weren't the same the summer after graduation, even though you tried to keep them that way? And how it all suddenly ended when college started, even if you DID try at first to keep in touch? I'll bet you've often wondered over the years what happened to those people--just like Kyosuke does with Madoka and Hikaru. After all these TV and OVA episodes, the _KOR_ characters are like friends, and now it's time to say goodbye to them, at least until _New Kimagure Orange Road: Summer's Beginning_. After all, an anime series doesn't last forever any more than a high school clique does. I'll bet many Japanese viewers who watched this movie back in '88 spent the next eight years pondering the fates of Madoka, Kyosuke, and Hikaru, not to mention those of the many supporting characters.
As for the resolution of the romantic triangle, the two things Kyosuke does toward this (confessing his love for Madoka and being honest with Hikaru) come so suddenly that we realize that he is finally overcoming his capriciousness and, well, growing up. All the times that Kyosuke has to keep rebuffing Hikaru are agonizing--it's like watching a terminally ill person refuse to die, and you wonder when it will end, or IF it will ever end. But at the end of the movie, everybody moves on.
The movie moves a little slowly during the first half hour, but this is because Kyosuke and Madoka are struggling with their feelings and realizing things are changing; the many brooding silences during this time tell us what they are thinking. And as the other reviewers have pointed out, neither Kyosuke nor his sisters use their psychic powers even once during the movie, nor is there any of the slapstick humor from the TV and OVA series--it's as if the series is growing up as well.
The animation seems slightly better than the TV series's, but, like the movie itself, it's nothing too flashy. So why are the beginning and ending in black and white? Maybe to indicate that as they are walking to the college, Kyosuke and Madoka are now sadder (but wiser)? Maybe to emphasize the fact that, as in the TV and OVA series, these events have taken place in the past, and Kyosuke is recounting them? Or an allusion to _The Wizard of Oz_, perhaps? You'll have to decide for yourself, just as for eight years the original viewers had to conjecture what happens to the characters after this movie ends.
At any rate, it's good to see everything finally resolved, even if this resolution does raise new questions. And be sure to watch the ending credit sequence.