That is, as "geometry" becomes more and more refined, there are questions of why the the continents are they way they are (Wegener's theory wasn't rejected until the 1900s!), why certain volcanoes exist where they are, why certain rock formations exist where they are, etc. That's why geology is still an active field.
There are no outstanding subtle questions about the Earth's geometry as far as I'm aware. It's not a perfect sphere but we have literally mapped the surface of the Earth with detailed 3D point clouds - we can model the geometry down to near arbitrary levels of detail, and we do. Look at Google Earth!
Questions about how the Earth got into its current state and why it looks the way it does are not geometric questions.