I thought they worked by dielectric heating? Making polar molecules get all frantic and stuff. There is a safety mechanism to shut off the magnetron when the door is opened, and a screen to make the viewing window opaque to microwave radiation, but those can malfunction.

[0][https://en.wikipedia.org/wiki/Microwave#Effects_on_health] [1][https://en.wikipedia.org/wiki/Microwave_burn]

Here is a video explaining: https://www.youtube.com/watch?v=7FhwTelc5Tg

The turntable in my microwave failed when I heated up a frozen pizza, and the result was part of it was burned, and part of it was still frozen.

As far as I know, that's the mechanism by which microwave radiation heats molecules, but the specific design of the oven is to produce standing waves so microwaves can become concentrated. I may be wrong, though.

Not wrong -- the safety screen is part of the cavity resonator. But if there's a hole in it, or if you defeat the door interlock, you can still cook yourself with microwaves. In general I'm not too concerned that I'm going to cook my eyeballs by looking at my spaghetti to make sure that it's not exploding all over the inside of the microwave.

Going back to the "discovery" of microwaves for cooking food, the story I heard was a radar tech noticed a chocolate bar melted in his shirt pocket.