In a rotating, spherical reference frame, an observer would experience three "fictitious forces" (called fictitious because in an inertial reference frame -- a frame which is neither accelerating or rotating -- there is no force present, and only appear as a result of your own acceleration). These fictitious forces are based purely on mathematics, geometry and vector arithmetic specifically, and are an inherent property of the geometry of spheres. Here is a derivation of the three forces (notice that the derivation has nothing to do with astronomy, gravity, Earth, or any physical example):http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node56.html
The most well known of these three forces is the Coriolis effect, which is the middle term, (omega)x(omega)xR where omega is the rotational frequency (how quickly and in which direction the reference frame spins), x is the vector cross product, and R is the radial vector in spherical coordinates (where R is the direction pointing away from a central point, theta is the tilt from an arbitrary verticle R direction, and phi is the azimuth angle).
As you know, the Coriolis force is responsible for the shape of hurricanes, but also their direction of travel -- hurricanes tend to move towards the equator. This motion ONLY HAPPENS if the R vector is spherical. On a flat frame, R points along a Cartesian direction which would cause a hurricane to always move the same direction regardless of where it was on the Earth -- contradictory to the observed motion which switches directions above the equator. Your model would need to account for this which it currently does not.