Generally speaking, the assaults on microwaves either suggest that the damage and de-nutrify food, or that the microwaves themselves are zapping us as we stand around the kitchen.
Let's take the food part first. It is certainly true that microwaving reduces nutritional value - but so does all cooking. On the whole, cooking in a microwave is more likely to retrain nutrients than using conventional means of cooking. Some of this is probably due to the reduced cooking time. Of course it's perfectly possible to cook vegetables for longer than usual in a microwave in a container with lots of water - and just like boiling vegetables excessively in conventional cooking, this is a great way to remove nutritional value. Like any other means of cooking, it's possible to microwave badly.
Another food claim is that microwaving produces carcinogens - again, this is a typical outcome of cooking, though unless you char your food, the amount of carcinogens produced is likely to be lower than the levels of natural carcinogens that are in food anyway. It is sensibly recommended that some plastics aren't used in microwaves, but this is because they melt, not because they give off nasty toxins.
How about the stray microwaves? Studies of undamaged microwaves have shown practically no leakage - well below safe levels. It is important to replace a microwave if door hinges etc. get damaged, but if your microwave is in good condition, the amount of microwaves that can leak from it is tiny and harmless. Those who don't like microwaves will always refer to them as 'radiation' because this sounds scary. They are indeed radiation, but only in the same sense that light, for instance, is radiation. We are not talking about nuclear radiation, but electromagnetic radiation - things like radio waves and light.
Nothing that makes things hot is totally harmless. You can get burned from hot food in microwaves. Microwaves are susceptible to uneven cooking - so it's important that you make sure the turntable is working properly and that you stir food as required. And it is possible for some liquid microwaved foods and drinks to spurt when, say, a spoon is put in them - so care is important. You shouldn't leave a microwave in the charge of a five-year-old, any more than you should a conventional oven. But all the negative comments about microwaves beyond this simple safety requirement seem to come from a very small number of sources, some of which have a vested interest in selling 'radiation meters' etc., while those regarding microwaves as safe are proper scientists, engaging in well-reviewed scientific trials.
- Burned food - page 15