Seems like something went wrong here.
Already tried to re-unwrap the wrong displayed parts of the mesh, also changing shading mode from smooth to flat and back to smooth. It still looks like this:
However, it seems like it actually doesn't have to do with the material shading. What else can I do to let it being displayed correctly?
Recalculating the normals did NOT work. It still only appears in "textured solid", pure solid mode shows the model like it should. Else no errors in the texture itself.