That was one of my more regrettable anime misjudgements. Learn from my errors. Don't watch this show.
I quite liked the first episode, which promised a time-travel mystery. Unfortunately I was getting a bit impatient by ep.6 and the show had lost me completely by ep.7. After that, I was just watching to get it all over with.
The show's problem is that it's based on a visual novel and driven by a weird, unintuitive model of time travel. (I get the impression that someone was trying to trump Steins;Gate, or at least wanted to do the same thing in a new way.) What it's not driven by is its cast. The characters don't really matter and don't get much to do. Watching this show is like watching the scriptwriter doing a jigsaw. It's intricate, but you won't care.
Our hero, Setsuna, wakes up naked on an island beach. He's got amnesia, but he knows that he's got to save someone and kill someone else. (He achieves neither and the show completely forgets about the murder thing, never even telling us who his target would have been.) This is an insular island that keeps itself to itself and is, frankly, kind of boring. Not much happens there. We meet some girls, each with her own inconsequential mini-storyline. Karen's the only one who does something interesting (leave the island), but then she immediately comes back again. Rinne thinks she's ill with "soot blight syndrome", but she isn't. Sara wants to murder Setsuna, but that's only for a few scenes (and ineptly) after which she forgets all about it.
By ep.6, the show had fallen into harem-style time-wasting. Stupid Hair (sorry, Sara) is indulging in stereotypical harem silliness, even if it's for a timey-wimey SF reason. (We also have no idea where she gets her odd reasoning from, or why she has such confidence in it.) Rinne's just as bad, although at least the episode's taking her feelings more seriously and not using her as a joke. The plot's degenerated into "Setsuna hangs out with girls".
The show finds a solution to that, but it's just puzzle pieces. Timeslip, mysterious island #2, Star Trek whooshing door, time capsule... yeah, fine, but what about the characters? Admittedly there's some guilt and self-sacrifice, but all that's really happened is "Setsuna hangs out with girls" changed to "Setsuna becomes an exposition-enabling device and plot puppet".
Apparently the original game has lots of time leaps to Fix What Went Wrong. That's approximately true here, but with a weird twist in ep.12 that lost me (again). I don't believe it. It's horseshit. I suppose someone might be wrong or lying (which does in fairness must be true of certain earlier theories like Sara's "I am my own child"), but I was simply rejecting what I'd been told. Why should things repeat so precisely? Why and how should the world have got into loops like that? (Apart from anything else, mankind's exploitation of fossil fuels has made it almost impossible for the next intelligent race to have a similar industrial revolution. The coal's mostly gone. We've burned it.) Why are there always duplicates of everyone? I suppose the best answer might be "reincarnation", which is a Japanese homophone for Rinne's name and could be linked with the mythological significance of Urashima island. There are also references to Avalon, another famous mythological island. You could build a theory around Buddhism. For me, though, it's unsatisfactory to have a detailed, intricate time travel (ish) story that doesn't make sense on its own terms.
I might be wrong, but I think we end up knowing nothing about what was going on in ep.1. There's lots of basic stuff that's never explained, in fact, e.g. who built the time machine in the first place. I believe the original game has more explanations (e.g. a nifty one for Soot Blight Disease that involves ice ages), but unfortunately I was watching the anime.
The apocalyptic totalitarian theocracy (eps.9-10) is entertaining. I'd have enjoyed twelve episodes of that, but unfortunately we know it's all going to be unhappened and/or timey-wimied away. The rewriting of ep.11 is theoretically interesting, but again the show's presenting jarring logical leaps as unchallenged conclusions. "If time travel is possible, more than one version of a person can exist." Whoah, no no no, wait. Run that by me again.
By now the show was annoying me. I haven't really gone into the cast because there's little to discuss. They're nice people, but the plot's treating them as spectators and puppets, not participants. It is, though, worth mentioning that ep.12 has a love triangle that nearly gets resolved with a romantic relationship between a father and his daughter, with the mother's blessing. The anime's backpedalling away from this as hard as it can (in a slightly implausible way), but apparently the game lets you take this relationship all the way to sex and marriage. There's also some overblown music.
I spent five episodes waiting for Setsuna to kill himself (having decided that another version of himself was the most plausible murder candidate in ep.8). I was disappointed when he didn't.
The show's first third is okay. Life's peaceful and mildly intriguing on that island, almost cut off as it is from civilisation. (They have shops, policeman and mayors, but you wouldn't have been that surprised if they'd burned Setsuna in a wicker man.) Ep.4 is the best episode, with Karen visiting the mainland. However I'd strongly recommend ditching the show after that. It's not even kitsch enough to laugh at, except in ep.12. Instead, underneath, it's a dry intellectual exercise that's unfortunately been adapted into anime.