Are you sure the normals were OK before you started converting formats?
It may sound obvious, but that seems the most likely problem. When I am modelling, I always have the normals displayed on the polygons ... so I know the normals are good.
I have never had a problem with normals yet as a result of the conversion process. I would expect, though, that a conversion problem would affect all or none of the normals, rather than patchy hit and miss flipping.
The bad polygons also seem to be triangles.... which rules out bad geometry.
There really isn't much more I can add. If you want, I can have a look at the mesh, which might tell me more. A picture only shows so much
