Miller indices are very simple and straightforward for most planes. However, I see a problem for a plane that goes through the coordinates origin. In such a case, the Miller indices should be $(\infty,\infty,\infty)$, because the plane intersects the point of origin at the point $(0,0,0)$ right?
Also, how would the Miller indices look like for a plane that is spanned by the vectors: $e_x$ and $ \frac{1}{\sqrt{2}}(e_y + e_z)$ ? The axes are all intersected at $(0,0,0)$ so the Miller indices should also be $(\infty,\infty,\infty)$. But this would mean that the Miller indices don't describe the plane unambiguously right?
