Hi Marc, also another alternative way is the following.

First I drew a circle in the Top view, and used that in a boolean to cut the latitude tubes, so that they were separate and not all overlapping each other at the poles:



Now that will avoid one area that confuses the booleans and those can be booleaned away from the sphere body:



The result model of that is attached here as "2008-07-23 - Globe_2.zip".

Now the latitude lines have the same kind of difficult area where they are touching the longitude ones at a kind of single crown point type thing, that is an area that is not currently handled well.

If you re-create those latitude lines using a slightly smaller or larger radius than the longitude ones, then those should carve out better.

But definitely that other method of building just one slice and replicating it will tend to avoid criss-cross pieces even more and probably work better.

- Michael