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jhuffman comments on Complexity of Value ≠ Complexity of Outcome - Less Wrong
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Moral realism is a meta-ethical view - I do not know that a such a viewpoint can be as a matter of fact correct or incorrect. Maybe an ethical realist would argue that it is a matter of fact, I'm not sure - an anti-realist might argue that neither viewpoint can be a matter of fact. The whole argument is really about "what are facts" and "what can be objectively true or false" so I suppose that someone may extend this view to the meta-layer where the merits of the viewpoint itself are discussed although I think that would not be very useful.
I'm going to deploy what I call the Wittgenstein Chomsky blah blah blah argument. Philosophy is just words in English; there is little ultimate meaning we are going to find here unless we declare our mathematical axioms. Already most of the views here seem reconcilable by redefining what exactly the different words mean.
To answer the question: some things can be proven objectively true, some things can be proven objectively false, some things can be proven to be undecidable. A fact is a true statement that follows from your given system of axioms. I personally am unsure if most moral principles or meta ethical systems can be declared objectively true or false with a standard ethical system, but I'm not going to take it seriously until a theorem prover says so. We are never going to convince each other of ultimate philosophical truth by having conversations like this.
I suppose this makes me an anti-realist, unless someone feels like redefining realism for me. :D
Again, it feels like I am missing something... http://plato.stanford.edu/entries/truth-axiomatic/ helped a little.