Most people did not enjoy this show. However, I did. Maybe my opinions are highly flawed. I doubt I'm the pinnacle of good taste, so you shouldn't take my review as the word of God. But the fact remains that I liked Rinne no Lagrange while many others did not, so here's me telling you why.
The plot of Rinne no Lagrange is not very complicated to begin with, at least not to me. A lot of people found it a bit confusing and the back stories not fleshed out enough, but keep in mind that this is a two-season anime. I expect, with the ending presented in season 1, the reasons behind what happened in these 12 episodes will be further explained. But overall, I found the story to be quite interesting. Basically, a girl named Madoka is chosen to pilot a mecha along with two other young girls. And stuff happens.
It's not unique at all, but I felt that the way it was presented was rather refreshing. Rinne is a show that has serious undertones and darker elements, without actually taking itself too seriously. It's a precarious balance between light-hearted and the somber, and I'll admit that this doesn't always work out so well. But while Rinne's story is far from perfect, I honestly did like it.
When I first started watching this show, I had to watch the early release version streaming. I honestly thought the art sucked. But once I began downloading episodes in higher quality, I realized that the art in this is actually very good. The special effects are all done beautifully, and while some of the daily life scenes aren't animated as well, overall I thought the animation was quite good. The character designs were all very interesting as well, and I liked the idea of giving the aliens multicolored "anime hair" while giving regular earthlings normal colored Japanese hair.
The music in Rinne didn't actually start getting good until the later half. The first few episodes had alright music, but in some of the battle scenes later on the soundtrack was just lovely. I liked the voice acting as well, so no problems there. There were times in the series when the uplifting string music gave the rather bleak images an eerie tone, but that was very minor and not often. Overall, the music was nice when there was music, and the acting was fine.
Depending on how you feel about moe, the character section will vary greatly for everyone. Madoka, Lan, and Muginami, the three young female protagonists, are clearly there to attract the older male otaku audience. They each have their own cute little quirks, and each of them have their "cute girls doing cute things" moments. However, unlike actual moeblob shows, the three girls in Rinne actually go through a lot of hardship and emotional suffering as the series progresses. There are moments where you know for sure they will be fine as long as they have each other, but there are many other scenes where you question whether or not anything would be the same again. It's not a "tear them up from the inside out" kind of show like another famous series with a protagonist named Madoka is, but the characters do go through enough development to make you laugh and cry with them.
I suppose this show doesn't appeal to everyone. It's not a universally likable show. It has tons of moe fan service (though very little of it is sexual), and seems to attract the older male otaku population rather than everyone. However, as a teenage girl, I can say that I highly enjoyed Rinne. I liked that it started out light and happy, with only a few glimpses at the underlying darkness, and just when you think it's all going to go downhill, it returns to being the same kind of cheery again. This type of emotional setup is not for everyone, and it will confuse a lot of people. But I liked it, and I found it to be rather clever.
If you are looking for a mecha show with badass little girls piloting giant robots and fighting aliens, then this is not the show for you. If you are looking for something more nuanced; something character driven; something that confuses your emotions but still leaves you wanting to know more, then by all means, watch Rinne no Lagrange. It's not perfect or amazing by any standard, but it's good. I can't quite explain in words how I felt overall about Rinne. But I suppose...it was good. Sometimes, it was just fine, and at other times, it was great. So...good would be the right way to express it.