I haven't uploaded your file, but did wonder if you can actually select those errant edges and surfaces in the 3 parts you first posted. In other words, are the edges, surfaces, etc., really in the 3-space location where they are rendered or is the issue that the display library can't handle the geometry for some reason and paints them in the wrong place?
Said another way, the actual part geometry may be OK, but the 3D rendering of them fails for some reason. I've seen some strange things like that occur in other 3D software when you get local surface normals reversed on one or two segments of a part and the rendering engine can't handle it.
When you select the wonky things in the Design Explorer, does every portion of it change color to show selection or just some parts of it?
Cheers,