The Second Half Of Death Note Is Good, Actually
The first half of Death Note ends when L dies; episode 25 of the anime and chapter 59 of the manga. Notably, this is 54% of the way through the manga, which is 108 total chapters, but 67.5% of the way through the anime. (The anime adaptation of Death Note is very faithful to the first part of the manga, but makes significant cuts and edits in the second half.)
A lot of people stopped watching at this point, and many people claim that the second half of Death Note is bad and/or pointless. After L dies, there's no point watching any more! So they say.
This position is based on a fundamental misunderstanding of what Death Note is actually about. Death Note is not about the cat-and-mouse game between L and Light Yagami. This is, I think, self-evident, on account of L dying halfway through the series. Death Note is about Light Yagami and a number of overarching themes. L is important and a central focus of part 1, but the fact that he dies is not bad writing or a mistake, and the story does not end at his death. He's not the main character! Light is!
After L dies and Light "wins," there is a timeskip. The world changes radically; it becomes a completely different place. Most countries in the world have officially ceded control over criminal justice to Kira, the crime rate has plummeted, war no longer exists, and people exist in a constant state of fear of being murdered by their tyrannical anonymous seemingly omnipotent god-king.
In part 2 of Death Note, Light has created a new world, of which he is the god. And this world is, bluntly: stupid. It sucks. It's ridiculous. The world no longer works the way it ought to. This is, in my opinion, not a mistake or bad writing; it is intentional. Of course the world Light creates is ridiculous and sucks. He is ridiculous and he sucks.
The main difference between Near and L is not that L is "cool" and Near is "lame" or "silly" - L is lame and silly. They both are weird freaks with a bunch of bizarre behavioral quirks and they are both genius detectives raised in a genius detective orphanage. The main difference, which guides the entire narrative thrust of the second half of Death Note, is that Near does not take Light seriously.
L is indulgent with Light. L enjoys playing with him, respects his intellect, considers him a worthy opponent in a grand game. This kills him. He knows early on that Light is Kira but he doesn't do anything about that; he lets him cook, watches him work, befriends him. He literally shackles himself to Light and is willing to make this permanent. He does not stop him. Much like a person with a wild animal for a pet, he lets himself believe that Light is special, that Light will not hurt him, that he's tame. And, much like a person with a wild animal for a pet, his reckless disregard for his own safety and the safety of those around him leads to his death.
Near thinks Light is an asshole. Near has no respect for Kira. Near is not playing with Light, not interested in Light's big brain, not interested in his schemes. Unlike everyone else in Light's life, Near does not find him charming, convincing, or endearing. To Near, Kira is just a murderer, and just like any other murderer he is going to arrest him for doing crimes.
Near is playing a game - with Mello. Light and his schemes, his intellect, his charisma, his stunts, is not important to Near. Near truly genuinely does not give a shit about this guy.
Light's success depends not only on him being smart but him being 1) handsome and charismatic and 2) lucky. Essentially, he gets what he wants because he's the main character. People let things slide that they wouldn't otherwise. They give him the benefit of the doubt. Various things just happen to work out for him when they could've easily gone another way. He believes that this is because he is the center of the universe; he's god, he's the perfect boy, he deserves it. Light loves the just world fallacy: good things happen to him because he deserves it, because he's a good person, and bad things happen to other people because they deserve it.
But to Near, Light is not the main character. L is willing to make Light the center of his world - like Misa, like Mikami, like his adoring parents and adoring sister and adoring classmates and adoring public - but Near is not. And this lack of respect, this refusal to take him seriously, this refusal to play along, completely crumbles everything Light spent almost a decade building.
And this is what Death Note is actually about: Light is a fucked up guy. He is wrong. And he loses. When he dies, it is pathetic. He's childish, a sore loser, selfish, sheltered, ignorant, and cruel. He's not god, he's not special, he's a murderer and he's high on his own supply. He thinks he is a hero, and that murder is heroic; he is wrong.
It's also notable and (again, in my opinion) good and intentional that unlike L, Near does not resort to cruelty in order to "win." L tortures Misa, puts Light and his father in solitary confinement, plants cameras in the bedrooms and bathrooms of underage kids - one of the first things he does after being introduced is use Lind L Tailor as a human shield. L makes it very clear that he does not have any problem doing any of this as long as he can achieve his goal. Near is not nearly so ruthless; he doesn't do any of that. Like L, he abducts Misa and holds her captive; but when he does so, he puts her up in a comfortable hotel room where she's out of the way and bored.
Near and Mello, like L and Light, are childish and rude and eccentric. But in them we also see that childishness alone is not a damning character trait; it is not true that someone childish and strange is always going to be a cruel megalomaniac, and that L and Light's faults are their own. Demonstrating by contrast!
The point of Death Note is for Light to lose, and for him to lose miserably and pathetically. One of the most important scenes in Death Note is when Light dies. It's not a noble death. He isn't martyred heroically, he doesn't go out in a blaze of glory. He loses all of his composure, he gets shot, and he starts screaming and crying and thrashing around. He sobs that it hurts, that he's scared, and begs for someone - anyone - to come and fix it for him. And they don't. In a mindless panic, reduced to a wounded animal, he does not face his own death the way he faced others. He runs until he cannot run any more, and then he dies. Light is not a god, not a superhero, not a noble messiah grandly taking on the burden of sin for the sake of a better world, he is a wretched pathetic murderer. He can dish it out but he can't take it. At his core, when you strip away his pretense and schemes and delusions, you are left with a frightened child who never grew up. That rules!!!!!!!!!!!!!!!!!!!!!!
Light sucks in the second half of Death Note. He's constantly sweating, swearing, caught off guard, frustrated. He's losing and he doesn't know how or why, too sunken into delusions of grandeur to even fully understand what's going on any more. He's nastier, more reckless, more obvious, and every moment of weakness gets pounced on by the unrelenting unsympathetic Near.
It is a very different dynamic from his dynamic with L. The second half of Death Note is quite different from the first half! But I do not think it's bad and I think that the majority of people who think it's bad Just Don't Get It.