Issue with hemisphere part with textures

[Travis Cobbs]

In particular I get that the vertex at the North pole (0 46 0) has UV value (0.5 0.13888888) which is in the middle of the land.

I'm not sure if you are referring to cylindrical or spherical mapping here. If the former, the UV coordinates are essentially undefined anywhere on the axis of the cylinder. (I think they have a valid V value, but their U value is effectively "all of the above".) If the latter, then I think the same thing happens at the north and south poles. When texture UV mapping is performed in advance, the U value can be calculated based on the U values of the other two vertices in the triangle that touches the pole. But for projected textures, I don't think this is possible.