If your using the more normal and newer vertex arrays, then you have faces which share the vertices at the ends of the globe. Texture coords are mapped to vertices and the texture lookup engine interpolates between them. You cant just add or subtract from the values at the vertices because at the two different times you need different values. So you need another set of vertices with the same position coords but with different texture coords.

If your using old school OpenGL with immediate mode geometry vertices then you will be entering the texture coord on the fly. In that case you need to ensure you don't wrap the texture coord value back around to 0 or else it will reverse the interpolation but instead use GL_REPEAT and let the texture engine repeat mode do it for you.