Ahh you have polys facing the wrong way. You might want to check creative crash for a script similar to this: http://www.scriptspot.com/3ds-max/scripts/unify-flip-normal-polygons It will unify your polygons so that backward facing polys get flipped to face the same way as the majority of the faces in the mesh. Doesn't Maya…
If you are using normals, make sure all your uvs are facing the right way in the uv editor Christer. :o otherwise it will reverse the normals or screw something else up. Try that. If it still doesn't work, send the file to me?
Yes Maya has backface culling. In the viewport menu -> Shading>Backface Culling Alternatively you can go into Lighting and turn off two sided lighting, this will show a black polygon face instead of a transparent polygon(possibly easier to spot). You can also verify face normal directions through Display>Polygons>Face…
Is there equivalent of Reset X-From in Maya? If so use it. In 3ds Max there is STL Check (used mostly for rapid prototyping) to help as well as xView which can help you determine a lot of errors quickly (open edges, flipped faces etc). EDIT: try to use automatic unwrap and render if it helps. EDIT 2: is that 3rd one normal…