So I decided to do some late night cooking, and almost succeeded in doing something spectacularly disastrous.
Basically, I turned on a burner, but SOMEHOW, even though I’ve lived in this apartment for many years and almost never use anything but the front burners, turned on the wrong one. Worse, the back one had, sitting right on top of it, the cover for the pot I was using. And, of course, I had the burner on all the way because I was boiling.
I only realized something was wrong when I heard a sharp crack. That crack came from the lid on top of the burner. The bottom is all metal, but the handle (circular and plastic — or similar material; I’m not sure — and screwed onto the glass dome part) seems to have melted and seeped through the hole through which the screw that attaches it to the glass is fitted. So now there’s this white residue over the burner coil and such.
First question: after a few minutes panicking and letting the lid cool (during which I scorched a dish towel and heated the linoleum on the floor more than it probably should), I turned on the fan over the oven and opened a nearby window. I think, THINK, the odor’s dissipated, but it’s been so long I’m not sure. This was about an hour ago. (The lid, at least, is now cool and no longer melting, so that’s not an issue.) Any health risk I should be concerned about, especially since I want to close up the window again (it is winter, after all)?
Second question: any reason I should bother getting that back coil replaced by the maintenance crew? As I said, I pretty much never use it, and the stove is so old (I’ve been here a very long time), the whole thing will most likely be replaced whenever I move out.
Random complaint: this is the second perfectly good lid I’ve destroyed. The other slipped off a pan and shattered by landing RIGHT on the handle. Now I have to buy another lid for the pot. 
But at least there’s no fire department needed…