It reads something like this (Anselm's original, as taken from wikipedia):
1. If I am thinking of the Greatest Being Thinkable, then I can think of no being greater
1a. If it is false that I can think of no being greater, it is false I am thinking of the Greatest Being Thinkable
2. Being is greater than not being
3. If the being I am thinking of does not exist, then it is false that I can think of no being greater.
4. If the being I am thinking of does not exist, then it is false that I am thinking of the Greatest Being Thinkable
Conclusion: If I am thinking of the Greatest Being Thinkable, then I am thinking of a being that exists
I'll grant 1 and 1a, simply because it's workable logic. The flaw in this argument comes with #2, which is an unsupported assertion in and of itself. if 2 is false, then so are 3,4, and 5. Perfection does not necessarily equal existence; in fact, from experiential evidence, nothing that exists in the physical world would meet a true definition of perfection.
"(insert special pleading and whining about how dietyX doesn't exist in the physical world)"
That's all lovely, but something that interferes with the physical world, as the judeo-christian god does, has to have a physical manifestation, at least in the form of energy, which is also not perfect. Energy in any given form is conserved overall, but lost to whatever system it inhabits through entropy, which doesn't sound particularly perfect to me.
Let's pretend for a moment that the physical manifestation of said deity was actually a carpenter-mystic in a remote corner of the Roman Empire about two-thousand years ago, just for the sake of the argument. I'm granting something here that I fully deny in other cases, but it makes it fun, and the post longer than a paragraph. If that were actually true, it would mean that the physical version of this most perfect being was subject to doubts, fears, and allowing itself to be nailed to a plank of wood after being beaten and humiliated. Again, this is not perfect.
More fun with perfection: this perfect being is supposedly perfectly omnipotent, and perfectly benevolent. That would mean that there is nothing beyond the ability of said being, and that said being is kind beyond what we can possibly conceive of as kind. Yet said being also allows nasty, horrible, evil things to happen on a daily basis (leaving aside all of those that are attributed to said being in holy writ and by fools like Pat Robertson). So this perfect being is either not omnipotent, and therefore cannot stop the evil that men do, or is not benevolent because it simply doesn't give a shit. Either way, not a positive argument in favour of its existence. Moreover, omnipotence is, in and of itself, logically contradictory. If you can do anything, you can then make an object that you cannot move, which means you aren't omnipotent (paraphrased Dawkins here, there are more eloquent ways of expressing that notion). The professor, when confronted with this, had to add a qualifier to the statement, claiming that the deity in question can do anything that isn't logically contradictory. Against this I would have to set a proper definition of omnipotence, and the list of logically contradictory things attributed to said deity.
Sorry Plantinga, despite my not wanting to read your drivel in the first place, you're still wrong on this one.