Boku Dake ga Inai machi - The Town where only I am missing. It's an interesting title, and it's also the title of a sad little essay written by an abused young girl within the show, about how her town would be without her alone - and how she doesn't mind that at all.
Reading that, you might be wondering what exactly the show is about. Isn't this supposed to be a show wherein the protagonist jumps back in time in order to find a murderer and stop him? Well, it is, but what makes the show so special is that it chooses to focus much on it's time on human drama rather than the murder mystery. Instead of having the focus be on finding out who the murderer is, the protagonist uses his knowledge from the future in order to help the victims - removing their 'alone time' so that the murderer would not have a chance to act. It's an interesting choice, and one that ultimately benefits the show.
The path the show takes allows it to have a very strong first half - probably one of the most emotionally powerful and great experiences that I have experienced in the medium. It's easily the high of the show, following the protagonist as he works to befriend and bring joy into the life of a girl who faces painful physical abuse at home to the extent that she wishes that she herself could simply disappear. This portion is aided by very strong visuals and direction, as well as the contrast between the short and painful scenes of home abuse compared to the moments and glimmers of hope and joy that the protagonist brings into her life. It's an arc that is both uplifting and painful at the same time - and something that could have perhaps worked even better without the mystery backdrop that the rest of the show focuses on.
Unfortunately, the rest of the show simply isn't as strong as that first half. As a human drama, the show is brilliant. As a thriller, it works okay, having many strong scenes with plenty of tension, plenty of little directional quirks combined with a conflict that the audience is easily invested in, making the show highly entertaining at most points, though the direction does go a little overboard into silly territory at points. As a mystery, however, it pales in comparison. Due to the setup of the show, the focus eventually has to shift towards answering the big question - who did it? Unfortunately, the show never really takes the time to set up potential suspects - it does take the time to throw a little suspicion here and there at times, but the 'answer' is really obvious as time goes by since there is only one plausible suspect. It simply doesn't function all that well as a murder mystery, making the later half of the show seem that much weaker as a result.
Although it might seem from what I have written that the show has two distinct halves, it must still be noted that the show does a fairly good job of maintaining its core thematic threads throughout the show, most notably though the growth of our protagonist - showcasing the themes of the importance of hope and believing in other people, as well as that of having the courage to take that first step to get to know others on a more personal level. It does portray it's message well, managing to wrap up the show quite well thematically.
Ultimately, is the show worth watching? Definitely. Although some might find the end result a disappointing one due to the initial hype that the first few episodes brought, it is still a very strong show that simply peaked really early on. Despite that, the rest of the show is still fairly good if unremarkable, and the high points of the show were easily some of the strongest and most powerful episodes in the medium. It's still a great show overall, and one that I would easily recommend any day.