Filletedge is an extremely weak tool. It won’t be able to make all the fillets correctly. If you use a fillet size of .005" it looks like it fails in about 10 places. Larger sized fillets fail in more places.
You can build all the fillets in Rhino that you need but that involves using the surfacing tools . You can also fix all the places that filletedge misses using the surface tools.
The best way to approach this if you want to fix the FilletEdge failures is first extract and copy to the clipboard the top and bottom surface. Then fillet all the boundary edges using filletEdge. Then extract the top and bottom surface again and delete them and paste the old version back from the clipboard. The reason for doing this is that filletedge trims these 2 surfaces incorrectly. Everything else trims and joins correctly so you can let filletedge do that. When you are all done making the fillets all the way around you can trim these 2 surfaces correctly with the borders of the fillets and then join it all into a solid.
The enclosed file shows how to fix up one of the spots where filletedge fails. All the other spots are pretty much the same deal.
Fix_Fillets.3dm (1.2 MB)