The majority of Watchmen is narrated by Rorschach’s journal. He is introduced as the only active masked vigilante who does not work for the government. He is seen as a protagonist, but he is ruthless in punishing evil. His ideology is that the world is only in black and white. There are no shades of gray. He exacts justice on those he thinks deserve it, and he believes that he has to because no one else will.
“You see, Doctor, God didn't kill that little girl. Fate didn't butcher her and destiny didn't feed her to those dogs. If God saw what any of us did that night, he didn't seem to mind. From then on I knew... God doesn't make the world this way. We do.” –Alan Moore
Rorschach points out that God, or anyone for that matter, does not watch the watchmen. They are able to do as they please, and their only obstacle is themselves. When he was made aware of Ozymandias’s plan, he is the one who saw his actions as evil, and insisted that they should be revealed to the public. But he is killed by Dr. Manhattan before he can do so. Is it wrong to kill someone for standing up for what he/she believe in? I think so. Even though he is an extremely right-wing character, he follows a strict moral code to determine what is right and what is wrong. And he uses it to also watch the actions of his fellow vigilantes especially in his investigation of the Comedian's death.