-minor spoilers below-
The first half of the show is the strongest, and the unraveling plotlines don't start to be very noticeable until the end of the nine schools competition arc. There is an aura of mystery around the protagonist and his little sister, which helps make them interesting but soon becomes annoying because there are hints of their story and motivations throughout the series, but it is never addressed in full. For instance, how did they come to their current situation, and what was their childhood like? THe opening and ending songs hint at it, but it is not addressed in the show hardly at all! In addition, neither the protagonist nor his little sister undergo a noticable character arc. I cannot tell you how they have grown throughout the series. This is partially due to the lack of a truly formidable obstacle. This isnt a strong issue at first because we still don't really know a lot about the character, but by the time the climatic battle comes at the end of the series, I can't help but feel a little disappointed/bored.
I'm sure the light novel paints a more complete plot and probably gives a little more background and character development. Its a shame that the anime didn't get a second season, because I feel the story would greatly benefit from it. This anime left me hungry for more, which is a good thing.
