How do cartographers attempt to deal with the problems with maps?

The Earth is a sphere, and true distances cannot be translated from a 3-dimensional form to a flat surface. Some maps are a form of the "gores" that can be cut from a globe to form a flat surface. But most use some form of projection that displays some aspects of the actual surface with some accuracy.

The smaller the area of the map, the less the curvature, which reduces the errors introduced.