I think the biggest problem in the definitions is that of necessity.
If necessity is conceived of as logical necessity, then the being referred to really does have to be logically necessary from it's other properties or the definition is self-contradictory and therefore logically impossible. And if we had good reason to think that the proposed "God" (a "maximally excellent" being IIRC) really was logically necessary, Plantinga's argument would be redundant. So, in this case we should conclude that the proposed entity is probably impossible.
If some other sense of necessity is meant we still have questions. Obviously we cannot define things into existence simply by adding necessity to the definition. We cannot dictate reality by such simple word games. So clearly beings defined as "necessary" are impossible, more often than not. And then we have to justify whatever concept of necessity is considered, and give reasons why it should be expected to apply to the proposed entity but cannot be applied to anything else.
So all in all, it seems to me that it is very unlikely that any proposed necessary being really is necessary.
Which leads us to the other problem with Plantinga's argument. It can easily be reversed. All we need to do is consider it to be possible that a Maximally Great Being does NOT exist. If we grant that, it follows that a Maximally Great Being does not exist !
From the arguments I have given it seems clear to me that we should favour the idea that a Maximally Great being possibly does not exist over the idea that it possibly does (because impossibility is more likely than necessity). Therefore Plantinga's argument weighs against the existence of God. At least to the extent it should be taken seriously.
Personally I think its main importance is in revealing the intellectual bankruptcy of religious philosophy - at least on the theistic side.