The first problem I have is mainly a matter of taste. The only female character in the series is the single most frustrating character I have ever seen in storytelling of any kind. Film, TV, books, videogames, you fuckin' name it. I have never wanted to put my hands around someone's throat more than Misa's, and I almost quit watching the series because of it. Every appearance she made, I would question myself: Why are you watching this in your valuable spare time? Do you want to spend your weekends and evenings angry? Some could argue that she is an excellent character FOR this reason--that she is written to incite these feelings and so she is a successful character. Frankly, IDGAF. She is hands down the most insulting female character I have ever seen and the strength of the story, in the end, could not make up for sitting through hours of her nonsense.
This brings me to my second major complaint about the story which is impossible to discuss without spoiling things at least a little, so maybe just skip this paragraph if you haven't committed to watching the series yet. My complaint is this: A character dies and the story renders this moment utterly meaningless because the character is immediately replaced with an identical character who behaves the same and fills the same role. A character dies and nothing changes or is achieved by it. That's writing for shock value. That's writing to betray your viewers. That's not writing that gives your story what it needs. After that event, the story starts to crumble because the engine driving it is broken. The new characters serve as carbon-copy replacements, but the viewer receives even less insight into their decision-making processes, and as a result, the mental chess match starts to feel more like a magical telepathic guessing-game. Conclusions are jumped to without being reasoned through, and the believability of the story suffers.
Further, the story rapidly gets out of hand around the middle of the series. Between the number of conditions, rules, and exceptions the viewer is expected to juggle in-mind and the number of times the Death Note changes hands, things get unnecessarily confusing and convoluted. I still swear there's a huge plot hole in there somewhere, but I'm never going to watch it a second time to pick it out. Suffice it to say that I think convoluted story-telling has a time and place (E.g., Baccano!), but that it's in poor taste to deliberately confuse your viewers. Confuse your characters and allow your audience to sort out the story through them as the characters learn what's going on, but don't keep your audience in the dark while all your characters understand what's happening. That's just inconsiderate writing.
A final, surface-level complaint is that while the style of art is well-crafted, the series is visually quite boring. An enormous amount of screentime is spent watching the main characters stare blankly and think about stuff, and there's very little movement and dynamism in the rest of it to make up for this. I feel that this story was probably better-served by the manga than the animation. That said, the voice-acting is ace and the soundtrack is rad as fuck and I'm gonna listen to it more times than I'm gonna watch the actual show.
In sum, Death Note is an excellent premise with emotionally-engaging characters that has a strong first half, but splutters out in its second leg. I recommend watching it once just to know what the phenomenon is about, but spend your re-watches elsewhere.
