Larky, I've observed one cup in the same location for at least three real-time days. And Arii, that was my first thought -- but you can't pick 'em up; once dropped, they seem to stay forever. I'm actually glad I drank the one I picked up in Bureaucratic Hall -- a small mood penalty was, IMO, much better than littering the world for (at least) days.
There was some bugs with them, yes. Some lingered for awhile.
I like 'em. Are they litter? Yes. Do they add just a bit of something to the game, one of those little things that makes the world seem... lived in? Alive? Not sure, but they work for me.
I am hoping that in the future there ends up being a forest fire or something that we all have to work together to put out. One tiny cup of water at a time.