The only reason the problem seems hard is you've used such a terse summary of events, and colored those events according to particular biases, that it would appear to be contridictory.
Would a person with a very great commitment to the law, be so cavalier about breaking it? The answer is pretty clearly, "No.", so it must be that Rorschach's fanatic commitment is to something else entirely. If we begin exploring the character a bit, I think we will probably find that there isn't as much contridiction as your summary would indicate.
But before we go there, I want to note that you can do this with any character, but doing it doesn't prove anything because the contridictions are false. I can take a character like Jean Valjean from 'Les Miserables', and say, "Jean Valjean is a hero and an honorable man, yet he is also a criminal and also evades the law? So which is he, lawful or chaotic?", and all I've done is create a false dichotomy using imprecise descriptions, and not proved anything about either Jean Valjean or the alignment system.
Rorschach is by the author's own estimate, "Extreme right wing", "anti-liberal" (alias 'socialism', if that makes it more clear), "anti-communist" (alias 'collectivism', if that makes it more clear), and "a nutcase" (alias, 'crazy'). We also know that he has virtually no respect for government, authority, or the law and that he self-classfies himself as a rebel and a dissident. He defines himself as a guy who says, "No."
He wears a mask that is always changing, but is always absolutes - black and white. Rorschach believes good and evil to be clearly defined and absolute, but tellingly he also considers himself personally to be the absolute judge of what is good and evil and holds himself accountable to no one and everyone accoutable to him. Also telling, his definition of 'absolute good' based on the causes he fights for (or against) seems to revolve around 'personality liberty, provided you do not harm others' (and if you do, then 'eye for an eye').
I consider Rorschach's alignment to be about as clear cut as any in fiction sense it very much was intended to embody a particular ideology. He's a slightly psycho anarchist libertarian vigilante. I think Rorschach is pretty much the iconic example of a Chaotic Neutral.
As further evidence of this claim, it wouldn't be very hard to go around the web to various right-wing Libertarian and Objectivist political blogs, and see them proudly claiming Rorschach as their own, identifying him with 'John Galt' and so forth. I'd link, but I don't want to drag this more political than it has to be (given that Watchman is openly political commentary). (I hope I don't have to prove an ideology briefly summarized as 'personal freedom is the highest good' is chaotic neutral.)
Additionally, Rorschach was based on a character named 'The Question'. The creator of that character was himself an Objectivist.