That article is one of the most egregious examples of know-nothing pseudosceince I've ever read. (Well, ok, I couldn't force myself to read more than the first few paragraphs.) For those who can stomach even less, the operating conceit is to first lead with shocking evidence that microwaving food can actually change its chemical structure!!, and to conclude that therefore there is absolutely no way to know whether it's safe or not. The notion that perhaps food chemists were aware of this fact already--even the notion that food chemistry exists--is completely alien to this philosophy of proud ignorance.
Microwaving food is perfectly 100% safe. And for god's sake, of course it changes the chemical structure of food--that's what cooking is.
Having said that, microwaved food--by which I mean packaged food intended to be cooked in the microwave--doesn't tend to be very good for you. Most of it is leached of its nutrients through mass production processes that place cost-effectiveness above all else, and try to make up for it by simulating flavor through the judicious addition of salt and the creepy magic of "flavorings": "natural" or artificial, they're the exact same thing: pure chemicals mixed in giant labs in New Jersey and added in parts-per-million quantities to make cheap food taste like what it tastes like. Strange but true: were it not for those flavorings that are added in such trace quantities that they're almost always listed 51st of 51 ingredients in your TV dinner, that TV dinner would quite literally taste like hot cardboard.
All of this is a bit disconcerting to a lot of people. Then again, being removed from the actual production of food as almost all of us are, most people would find it disconcerting to follow almost anything they eat from the farm/nature/plant to their mouths--much less traditional natural foods like sausage, much less foie gras. The problem isn't so much that it's disconcerting, but rather that it's low in nutritional value: much of the good stuff is processed out, and doesn't get added back in along with the salt and flavoring.
On the other hand, there's nothing about processed/microwaved food that is actively bad for you, unless you're among the minority for whom high salt intake can lead to high blood pressure. (And it tends to be higher in trans-fats than more natural foods; more bad on the heart disease front.) It's really just that it's low in stuff that's actively good for you.
In other words, there's nothing in microwaved food that will, say, give you cancer--not even trace quantities of some chemical shown to elevate cancer levels in mice given billions of times the concentrations. On the other hand, eating a spinach salad instead will significantly reduce your risk of cancer.
And, sad but true, eating a lower calorie diet in general will simply make you live longer--metabolism is apparently closely linked to if not the primary factor in cell aging.
Bottom line, what you eat has a huge amount to do with how healthy you are. But microwaves are no more and no less dangerous than the food that gets put in them.
(Ok, so microwave cooking can tend to destroy more nutrients than other methods of cooking. On the other hand, the char you get when you burn something on the grill is an active carcinogen. Point is, if something seems healthy--as in it tastes that way and you feel good after you eat it, not as in it comes in a green cardboard box--it probably is.)
(Final tip: you'd be shocked and amazed how many fine restaurants have microwaves hidden in the back. Well, scratch that--the answer is essentially all of them. You'd be shocked and amazed how often they get used.)