On “stale” coffee
The scene - Company cafeteria. There are a row of coffee pots. You pick up a cup and pick a pot and pour coffee into your cup. But there’s always a few options and you can see a coffee level gauge on the front of the pot that indicates just how much coffee is left.
I’ve been regularly going for the highest level (ie. the most full) coffee pot to get my coffee, figuring that the ones closer to being empty have been up there longer and therefore are not as hot/fresh.
You’re doing it right. Not only are the full pots likely to be the freshest, but there’s another issue that you’re conveniently avoiding with hot-plate coffee makers (those that heat the bottom of a glass carafe for a while after the coffee’s made, rather than insulated metal thermal-carafe pots that aren’t heated from below).
Applying more heat to coffee that’s already brewed degrades the flavor, making it more bitter over time. (This is one reason why percolator coffee is so bad: it’s continuously recycled and reheated through the entire brewing cycle.)
Black coffee doesn’t “go bad” otherwise — I once drank from a cup of great coffee that was left in my car overnight in the winter, and it tasted great, despite not being at an ideal temperature. (Obviously, the rules change if you add dairy, sugar, or very hot weather.)
When people pour a cup of “old” coffee from the office drip pot, it tastes bad because it has been toasted for a few hours by its carafe heater, not because of its age.
The effect worsens as the coffee level in the pot decreases: the same amount of heat per unit of time is applied regardless, so the lower the coffee volume, the more heat is applied to each unit of volume.
So the worst coffee you can get is the last cup of a drip pot that’s been sitting there on its heating element for two hours.