[Since writing this review originally, the two specials of Death Note Rewrite have been merged, this review refers to the first episode: Genshisuru Kami]
For all those who've seen the main TV series, this special episode is essentially a summary of all the events leading up until the end of L's arc in the overall story.
Story (8): Nothing new really. It simply takes the events of the main TV series and compresses it into the space of a little over 2 hours. I gave it an eight simply because it is essentially the overall story line which I was already familiar with. At first, I was a little bored to some extent with the story as I felt it was simply a bit of a cheat from the makers as, although it is meant to be the story told from the point of view of Ryuk, it just seemed like a shortened version of the story and didn't have the Ryuk-oriented spin which I expected. It does have some new scenes in there but they probably only constitute for about 15mins of the 2 hour 10 min running time. Unavoidably also, is because of the inevitable shortening of length you sometimes miss out on some of the more comical aspects of the show (in particular, that related to Matsuda and Misa).
However, if you can get past those facts, you can actually start enjoying it. If you watch it as though it is a summary of L's arc, then you'll likely enjoy it more than if treat it as some new item.
Art (9): All the same kind of animation from the show (which was very good), since it uses mostly the clips from the show.
Sound (9): Again very good. Uses all the original music and has the same voice actors for all the new, added parts. What I did like was the way that they managed to creatively use some of the music from the series to enhance certain scenes (e.g. the use one of the themes in the scene when chasing down the Yotsuba Kira).
Character (7): I gave this only a seven as I didn't feel the characters developed as wholly as they did in the series. For example, you didn't really get to the 'cleverness' going on in the battle of wits between L and Kira.
Enjoyment (7): I would say I enjoyed it a fair bit, but as mentioned above, it was nothing much new that I hadn't already seen.
Overall (8): If you're a fan of the series then I would say that this is probably a good recap for those who want to watch the series again but perhaps don't have the time to watch it all. A few more new scenes and maybe told more from Ryuk's point of view and it would have been a 9, but otherwise still a relatively enjoyable couple of hours.