try different settings in Rendering\Device -> Geometry cache: set "Never: (restart ZM, check the file), then set "Always" (restart ZM and check the file again).
Also, try changing object's mesh\vertices\format by adding "color", "deformable", "rigging + 4 bones". it might be related too.
also, does 3D/Perspective view shows this problem on solid polygons or on wireframe only?
Edit: I'm away, will be back tomorrow.