Light was wrong because he operated under the juvenile assumption that crime is a cause of immorality in society, instead of being a mere symptom of it. Thus, even if he does hang an extremely effective death sentence over the heads of all criminals as a deterrent, people will still commit crimes for the same reason people randomly kill each other now. Futhermore, Light only killed criminals who were reported in the media, so his judgements were also less effective in the sense that it encouraged a lot of premeditated crimes to become more secretive.
IN ADDITION, the biggest hole in the story is the fact that Light, whom despite being heavily studying law, is oblivious of the very basic concepts of the legal system. He overstepped the legal system that had been created and refined over centuries, by the people. Instead of letting society decide what punishments are acceptable, he tossed out the rational opinions of everyone around him and made his own rules about who deserves to die.