I think that you could always figure out what all of the corners are.
borginator2 wrote:Since all moves tend to move patterns of 3 or 4, I suspect that those 3 edges should prove the problem, although I suspect the other corner can be calculated.
You're right; those edges would be a problem. If you do (R B)(M U M U M U2)(M' U M' U M' U2)(B' R') to a solved cube, this is what you get.
Now, when you rotate the cube so that the other three sides are shown, this is what you see.
The puzzle looks solved but it isn't.