I guess I would have given this book more stars if the author hadn't made so many mistakes. And I'm not speaking of typos but rather of the logic in the book.
Mello is the narrator of the story. This doesn't make any sense at all, because Mello never knew either Beyond Birthday (the murderer) or L. (I mean, sure he heard of them, but he never actually met either, so how come he tells the story? Doesn't make sense.)
In the prologue (or foreword or whatever it was) Mello is foreshadowing L's death in the series and HIS OWN. If you tell a story, you usually are ALIVE, right? So how come dead Mello's telling stories from his grave? Seriously, there should have been a neutral narrator.
Then their were several other logical gaps. Naomi Misora, for example "prolonged" L's life in Death Note (the manga), because Light didn't know about the deep connection between Naomi and L, which he could have used for his merits. Death Note: Another Note states that Naomi made L's life a few years longer. That can't be, because the official DN timeline states that L dies approx. 1 year after first beginning his investigations about Kira. So when Light/Kira meets Naomi and kills her afterwards, L has at most 1 year left to live and not many years.
There were several other logical mistakes which made me ask myself if the author had actually read the series at all, but the biggest mistake was this one:
The novel introduces Rue Ryuzaki as a side character. Ryuzaki presents himself as a private detective. Naomi is a bit suspicious of him at first, because he has strange manners (sitting around hugging his legs, eating sweets all the time and crawling around on the floor), but L tells her to work together with him, so she does.
The thing is, the reader (as the he is meant to be) immediately assumes that Ryuzaki is L. This makes sense, because not only does L present himself as "Ryuzaki" in Death Note, but the way he acts is also strikingly similar.
Of course, the author wants the reader to think that Ryuzaki is L, but Ryuzaki is actually Beyond Birthday, the killer. That would have been a great twist, had it only been logical. But it wasn't. Another Note clearly states that B.B. doesn't know L personnaly. Which means he doesn't know anything about his habits or about what he looks like. So how come he guessed all of it? - doesn't make sense.
Even if the reader is supposed to assume that L assumed Ryuzaki's name after winning against B.B., taking over his "manners" would be completely out of character for L.
Especially since L is described in the end of the book as the "original" Ryuzaki, who was only the copy. But how could B.B. have been the copy of someonce he never met?
This book could have been good if only the author had at least tried to be logical. I usually overlook that kind of thing, but in this particular novel, I simply couldn't. Death Note: Another Note was so illogical I wanted to bite the authors head off.