This argument is very complex, involving a very long and tedious derivation in modal logic that I don't really understand myself, and so I'm not going to attempt to give it or even explain it. Suffice to say, the argument involves a controversial premise called the Barcan formula (◊∃xFx → ∃x◊Fx), or in English; if it's possible that a property be instantiated in some thing, then there exists a thing that possibly instantiates that property. When this was pointed out to me I found it quite unintuitive, but wasn't ever quite happy with the counterexamples I could come up with. But now I think I've come up with a strong counterexample that even the most stubborn theist couldn't deny.
Prior to creation, God—an essentially perfect being—was alone. Of course the property of imperfection would had to have been possibly instantiated, or else God couldn't have possibly created us; beings that sometime down the road became imperfect (if we weren't already from the start). But if this is the case, then prior to creation there was a possibility of imperfection while the only thing in existence was necessarily perfect, and thus could not possibly be imperfect. And so there's some condition (to the atheist a hypothetical, but to the theist it's very real!) under which the antecedent of the Barcan formula is true, but the conclusion is false. And, as everyone knows, that means the Barcan formula must itself be false. And, finally, since Maydole's ontological argument relies (at least from what I've seen) on the Barcan formula, the argument as a whole must be unsound.
Here is another: Because evil is possibly instantiated in us, prior to creation there must have been something that possibly instantiated evil. But God is essentially good, and thus he cannot possibly be evil. Of course only persons can be evil, and so prior to creation there must have been a person who was not God. Uncreated persons are gods, being eternal and self-sufficient, and therefore if the barcan formula holds and evil is possible, then we're left with polytheism.