The thing that really got my attention wasn't the assertion that there are some arguments in favour of realism, but that there are good arguments specifically against anti-realism.

But surely an argument against anti-realism is also an argument for realism? I'm interpreting Toby's comment as saying that there are good arguments for realism in general, but not for any particular realist meta-ethical theory.

Again, didn't get much from a quick skim, let me know if you find any real meat in there.

The author says in the conclusion, "I do not pretend to give any knock-down argument in this chapter for the thesis that objective moral facts or reasons exist, independently of our thoughts and actions." So I think it's mostly a matter of how convincing one finds the argument that he does give.

It seems likely, given that the author is a specialist in and proponent of moral realism, that he would give the best arguments that he knew, so this paper seems like good evidence for what kind of arguments for realism is currently available.