Not saying Death Note has the best writing around but it's appealing and entertaining. Some people that are not usually into anime liked it and I think that's a great achievement.
Characters did behave in a way that could be illogical but it was always within what the character was supposed be. Yes, characters "guessed" what others would do but that was the whole appeal. I mean, very similar stuff happens in BBC's Sherlock Holmes and it's regarded as a really good show (I think?). Specially in the episodes related to Moriarty.
I have found that the only way a show can be truly unpredictable is if they can take routes that could be seen as illogical. It's hard to write something exciting with that length without taking some liberties.
All in all, I'm willing to sacrifice perfectly consistent and logical writing for something to be entertaining.