I'll try not to keep things too long. Having just finished this series, I can say this: Kannagi is an extremely entertaining 13 episode series, and nicely done too. Here's why I think so:
Story: 7/10
I'll admit, in terms of story, Kannagi certainly does not progress much, most of the episodes consists of mainly comedy and slice-of-life aspects that are rather standalone and move the plot slowly. Interesting themes and subjects are brought up but not touched upon frequently enough, I can understand those who were unsatisfied with that. However I do think that Kannagi's strongest aspects lies not in its plot, but rather the comedy and interaction of the characters in the series.
Art: 9/10
Art and animation wise, Kannagi excels in this department. I was very impressed with all the fine details given to everything from Nagi scratching her leg occasionally as she sits to hair blowing in the wind to the electronic noise usually present in old analog television sets. Movement is fluid and natural and the characters and their surroundings are drawn consistently every episode. Not many still shots or other effects are used in place of actual movement.
Sound: 8/10
The music used in Kannagi is good, it fits their respective scenes and help add to the overall atmosphere. Th variations of the main theme as well as the instrumental versions of the OP/ED are pleasant to hear and give me nothing to complain about. The OP/ED themselves are catchy and very different from each other. All the voice actors also did an excellent job in bringing their characters and their personalities to life.
Character: 9/10
The cast of Kannagi each have their own unique personalities and quirks, most of which had me laughing as I kept watching. Development wise there isn't too much of that, save for the two main characters of course(even that was not too much). It is the way they interact amongst each other that deserves a 9 for character. There will certainly be someone you can relate to or situation they end up in that remind you of something similar.
Enjoyment: 10/10
In terms of enjoyment, Kannagi presents lots of it. Each episode has comedy to have you laughing, likeable characters, parodies/references and even some drama to top it all off. Personally I enjoyed every minute of Kannagi and in my honest opinion, you have to stop thinking of its lack of lot development in order to enjoy this series fully.
Overall: 9/10 (10/10 to me, but I'm trying to be more fair here)
Overall, Kannagi is a pleasant, thoroughly enjoyable experiece, be it the slice-of-life situations, comedy, parody/references to popular culture, brands and etc. to the characters themselves. Sure, for a 13 episode series the plot barely moved or resolved but honestly with the above mentioned things I feel that they nicely make up for it and is much more enjoyable when you overlook the pacing of the story. Probably one of the most enjoyable anime this year(certainly is to me )
You are not obligated to fully agree with my ratings and opinions nor does this review truly reflect what this series is like. Hope you enjoyed this review.
P.S. It's a Sony! ;D