what they have in common are "structures" inside the object and what's worse, most of the mesh manipulation programs declare them "ok" and can't "fix" them. netfabb, netfabb professional, meshlab, art of illusion.. they all see them as "ok" meshes
they normally work ok in other slicers but that's irrelevant, in s3d using "merge all outlines in single solid model" often works, but again, often does not. for e.g. the sample object I linked does not work ok.
The only "free" way I figured how to "fix" these objects so they can work ok in s3d is to import them in "3d builder" app that exist in win10 and do "edit/merge", this will merge all shells in the part into one single shell and the exported part will work ok in s3d. The solution works good but requires win10 and that's not always accessible, takes a while to boot up the vm etc.. so having something like this in the s3d itself would really be good