Correction – having done a more thorough analysis, it’s not the subsurf modifier that’s the issue. I hope this is helpful. Source code / objects available on request.
In each of the following pictures, the left-hand object is .blend->OgreXML->JME, and the right hand side is .blend->JME. The scene is lit by an ambient lamp and a directional lamp in JME – there is no lighting in the blender object.

Simple cubes (above) both seem ok, except the OgreXML one is much brighter.

Applying subdivide-smooth in Blender (above) leaves the object weirdly transparent in the OgreXML import, but it looks perfect in the .blend import.

Next adding a surbsurf modifier, above, has no effect on the .blend, but does on the ogre import. The transparency issue still remains.

Applying the above subsurf modifier, so it changes the mesh and removes the modifier, fixes the subsurf modifier for the .blend import. (The colour change is incidental.)
Finally, our corrupted geometry problems arise when a second modifier is applied: Multiresolution. I use this to improve the smoothing, but apparently it sends JME haywire for the .blend import.

In summary, the problem I originally reported is due to the Multiresolution modifier breaking .blend imports. The operator does not cause similar problems for the OgreXML import, but for some reason I’m getting undesired transparency in all Ogre XML examples shown here.
I hope this helps to improve the importer.