The easiest disproof of the ontological argument for the existence of God is to say that “existence” is not a predicate.
Another, potentially more satisfying route: go back through the Monologion and note all the times that he points out that infinite regress and mutual definition are complete nonsense, requiring every rational person to affirm the existence of God. In Lacanian terms, Anselm is proposing God as the master signifier or “constitutive exception”: God is both that which is beyond the good and that which provides a sharp boundary to that realm, both that which has no necessary relations to anything and that to which everything else is necessarily related. As Zizek has repeatedly pointed out, however, we appear to be living in a universe that actually follows the logic of the pas-tout, non-all or non-whole. A critique of Anselm in this direction wouldn’t just circle a single mistake in red — it would undermine the whole thing by pointing out that we do live in a universe of undefined boundaries and mutual definition (what people designate as a “relational ontology,” though they don’t often push very hard on it).
[People thought it was wrong when I said it a couple years ago on The Weblog, but I still think that you can explain about 90% of the function of the “God of the philosophers” as plugging the hole of infinite regress (of which mutual definition would be a subclass). At least up to Descartes — I’m not sure what’s going on with Spinoza, honestly, though I know he’s the main counter-example. He’s on the reading list.]
[When I originally came up with this idea, I was thinking in terms of undermining Anselm by means of Nancy, but I figure the Lacan stuff is closer to being common currency among readers of this blog.]