This film contains such a broad spectrum of emotions. I actually had a copy of this a while ago but never got around to watching it properly; I just flicked through it to get the gist of it - only, I didn't get the gist of it at all. Each part of it is quite misleading to the over all feeling and flow of the story. Now, having watched it properly, I can see this.
When you start watching it, it's a lightly comic slice-of-life thing. You're introduced to the various characters, mainly the heroine Makoto, and it's easy to believe that the whole film will just be this nice, heart-warming school life drama. Without wanting to give too much away, this isn't the case and after a fairly long intro, the plot proper kicks in and you really start to appreciate the slow build-up and low-key presentation of the film so far; it really grounds the consequent sci-fi plot and helps it become the philosophical piece it is, rather than just a novel movie about a kid that can leap through time.
Much of the plot could have been brought about without the time travel element; for example, when Makoto learns of someone's feelings towards her but then leaps back to before the confession, the same effect could have been achieved by simply having her overhear the guy telling a friend that he likes her. The impressive thing is, though, the time travel never feels like a gimmick, never feels bolted on or superfluous to the plot. If she'd merely overheard and done nothing about it, it would have remained a simple drama; since she goes back to a time before the confession, something much more tragic and regrettable takes place.
This is just one of many leaps that Makoto makes to avoid things happening, some in the "oh no I burnt my toast!" magnitude, and others far more serious. Seeing her be flippant with her powers makes it all the more affecting when things get serious and she realises her powers aren't just a toy for her to play with. Like so many great anime films, it manages to be a powerful allegory and a potent drama at the same time, not sacrificing any quality for another.
The only faults I can think of are that, yes, it is a little slow to get started and this may put off some more impatient viewers. Really, don't be put off if you feel your interest lagging early on. Enjoy the light-hearted stuff for what it is and realise that it'll only add to the impact of the more serious stuff later. The second fault is similar to the first; it's a pacing issue. Once the plot has laid itself bare in front of you, when almost all the plot twists have, uh, twisted, the story slows right down and almost lets the tension and drama its created to this point slip away as it slightly flounders towards its climax. It's not a big deal, though, and to be honest, as long as your heart is still beating, you should be sufficiently adsorbed and enthralled by the end to not really care about a bit of bad pacing.
In case you're wondering, this is an anime that will appeal to all sorts of people, all genders, all ages, anime fans and people who still think of it as "those Chinese cartoons". The romance is very affecting without being tacky or self-important. It has positive messages but never gets anywhere near feeling preachy or pretentious. It effortlessly slides between comedy, drama, romance, sci-fi, philosophy, slice-of-life and, I guess, thriller, without you realising it's changing. Considering you can get it for just under the price of a packet of fags (at the time of this review), you'd literally be mad to miss it.