But this is just the tip of the objection -- the broader objection is that this is English we're talking about here. English, the language of "women," of "colonel," of "laughter" and "slaughter," of "get" and "gem." As reader Brian Dulisse points out, "forte" can be pronounced "fortay," "fort," or "fortee." "This pronunciation is wrong because it doesn't match the spelling" isn't much of an argument in English.
It seems to me that the only sensible answer to "What is wrong with 'nucular'?" is "This is not the standard way that high-class people say it," coupled with "This term is a shibboleth that high-class people, and those influenced by them, use to sort those they'll call 'high-class' from those they'll call 'low-class.'" That's all the "wrong" there is here. Yes, I know this sounds like a leftist cultural critic position; but sometimes, as here, the leftist cultural critics are right. One day, "nucular" might be treated the same as "ah" for "I" or "crick" for "creek" -- a regional accent that's not wrong, but just different. It might even become the "correct" pronunciation, with "nuclear" sounding archaic or affected. It won't flow from a change to logic or morality, only a change of attitude by enough people in the influential classes, or by a change of who counts as the influential class.
So what of it? Well, if you're teaching a child (or an adult) to speak, of course you should teach him to say "nuclear," simply as an instrumental matter -- sounding high-class is usually (not always, but usually) more profitable, especially where the shibboleths are concerned. If you're making a purely esthetic judgment, well of course you're free to say "'Nucular' sounds ugly to me," just like you can say "Picasso looks ugly to me" or "Broccoli tastes bad to me." And if you're trying to infer a person's educational level from very limited data, you might use his pronunciation as something of a clue, though be careful: As I understand it, quite a few educated Southerners use this term (consider Jimmy Carter and Bill Clinton, both to my knowledge quite well-educated).
But before one says that "nucular" is "wrong," one should keep in mind just what a narrow and not terribly appealing definition of "wrong" one is necessarily using.