when the end containing her eye or mouth--for with us these two organs are identical--is the part that meets our eye, then we see nothing but a highly lustrous point
So in other words I was right to say that Flatlanders have a single mouth / eye organ; there really are all sorts of evolutionary snags, but if Abbott actually says it I suppose I have to go with it. I should have checked it the first time it came up.
Fortunately I haven't said much about this yet, so it won't be too hard to change things. There can still be specialised parts of the mouth for different purposes - transparent jaws, optical sensors around the perimeter, and some sort of vacuole system to get the food out of the way. I know it sounds a bit icky, and I'll try not to get too gross, but it looks like I'm stuck with it.