Pardon me. I deleted my comment before I noticed that someone had replied. (I didn't think replying to Constant was going to be beneficial. To be honest I didn't share your perception of interestingness of the conversation, even though I was a participant.)

What the hell does it mean for something to be objectively wrong?

Very little practically speaking. It is a somewhat related concept to subjectively objective. It doesn't make the value judgements any less subjective it is just that they happen to be built into the word definitions themselves. It doesn't make words like 'should' and 'wrong' any more useful when people with different values are arguing it just takes one of the meanings of 'should' as it is used practically and makes it explicit. I think the sophisticated name may be something related to moral cognitivism, probably with a 'realism' thrown in somewhere for good measure.