Dudes, if you're reading this page full of spoilers please don't blame me for continuing.
What makes Death Note good anime and reason why L's character is so brilliant isn't his intelligence, cleverness, him devouring ton of sugar and still staying slim. He needs to be super smart to fight Light, but he's such great and loveable character because he knows Light is guilty yet gives him the chance to repent himself. L treats Light as his only, genuine friend and is willing to forgive him. After Light kills him, he's changed man. Basically I see second season from Light's perspective as him wanting to be caught, because of what he did to L. He considered L to be his only friend as well but was too scared what will happen to him, he let his selfishness ruin his friendship.
First part of anime isn't about super smart dudes outwitting each other, if it was just about that DN would be crap anime just like second season is. Friendship is the reason why it is good. Without human, likeable characters, second part fails so bad. Mello isn't likeable char at all, but he's closest to it. Especially compared with emotionless man child called Near.
L sacrificed himself, put himself in the open unprotected. At that moment he let himself depend on Light and that cost him his life. I don't bite the story that he needed definite proof in order to put Light behind bars. If he wanted it that bad he'd find it sooner, Light was getting sloppy and left ton of clues. L isn't someone who needs everything to be perfect in order to put criminal behind bars, he knew Light was guilty because there wasn't anybody else who fits the profile. But he liked Light too much and enjoyed their little game. He valued playing with Light more than putting an end to his shenanigans. Some may call his actions stupid, I think he's very humane and awesome character.