Update.
I've been playing with it some more and I don't know if this will clarify or confound.
This time I was just creating a polygon, not editing one. If I create two points within a couple of centimeters (on my screen; it doesn't matter if I'm at 1:100 or 1:500,000) of each other the first point will disappear. If they are farther apart, say 5cm, the shape behaves normally. So I can make a 5cm x 5cm square, but if I were to try and make a 2cm x 2cm square, it goes nuts.