Let's just get one thing out of the way. The film's gorgeous. I think pretty much everyone can agree with that, even if not everyone was a huge fan of the movie itself. Eye candy through the roof.
But onto the story. Going into this movie, what I was looking for was something that would make this film... necessary. What I mean by that, is the film needed to do something that added to the story such that the whole story would be rendered incomplete without it. Too often, sequels to completed series don't accomplish that. Instead, they feel, at best, a separate story tacked on to the original. At worst, the sequel actually detracts from the original when included as pieces of the same whole. A recent example is Eureka Seven AO. It was unnecessary and damaged the main character from season one. I was hoping that this movie could avoid that.
Now, in trying to figure out how it could add to the story, I had to figure out what the original story was about. And, in essence, their are two main components. First, you've got the story of the magical girls. It's about everything that's going on with them in general. Who they are, what they are, what they do, what they become, how they become it, etc. Second, it's a story about the relationship between Homura and Madoka (from the perspective of Homura, generally speaking). Their are specifics in those two points, which I will probably touch on later, but those are the two major plot lines in Puella Magi Madoka Magica.
For the film, there wasn't a whole lot that could be immediately done with that first plot point. Madoka took care of that pretty well at the end of the series. The only thing we could have seen was the world operating under its new rules. Ironically, you don't see any of that in this third film. Instead, you see an altered world within the world that resulted from the original. You never actually see the new world save for brief snippets. You certainly don't see people operating in said world (except for maybe Kyubey, I suppose). All we get is this fabricated world, which is a little disappointing, but not a deal-breaker by itself.
However, there was plenty to do with that second point. The series even hinted at Homura, burdened with her knowledge of the changing world, wandering around this new environment. So yeah, plenty of opportunity there. This film was the chance to bring Homura's relationship with Madoka full circle. And, honestly, this movie exceeds. It's a slow build to that issue, sometimes seeming more like fanservice than anything else, but all the hints are there that the world in this film is a fabrication. The reveal, admittedly exposition heavy, played on both the new rules of the universe, brought the villain back in a big way, and quantified Homura's feelings for Madoka in a way that wasn't fully explored in the series.
But of course, that wasn't what made this movie controversial. No, what drove people to either side of the fence was the result of Homura's new outlook on her feelings. She believes that the only way she can truly express her feelings for Madoka, the only way she can truly protect her as she always wanted, was to become her antipode and pull her from her role as god of the new world.
And here's the problem with that: It's incomplete. Horror and tragedy may be a part of its modus operandi, but Madoka Magica did not end on that note. It ended on a hopeful note. This film takes that ending and, in the last moments of this film, reverses it to a tragedy. Even more than that, Homura and Madoka's relationship plot line still isn't complete. We see nothing of Madoka's perspective other than the promise of resistance at the very end. Even more so, Homura is a brand new villain. She just assumes that role at the very end, and nothing is done about it.
In short, this story doesn't work as a trilogy. It needs a fourth movie to tie the string it introduced in this film. And, to be honest, that's the impression I got from this film. It seems very likely to me that a fourth film is on the way. And if that film delivers a solid conclusion to this new threat, then it could work. Without that fourth film though, I can only recommend people watch the original series. I only hope that the hypothetical sequel finds some new ground in its lore to tread. Otherwise, the first plot line might overstay its welcome while the second one finally gets wrapped up.
Here's hoping.