I took a look at a few of these files to see if I could help.
The issue with the gear STL file that the original author attached is that it's actually 2 separate STL files in one mesh! I took a screenshot to illustrate this. So you are essentially telling the software to treat both of these parts as a single mesh, which isn't correct. That single mesh would have many self-intersecting surfaces since you actually have 2 parts squished together that overlap. The software identifies a bunch of these problems if you go to Repair > Identify Self Intersecting Surfaces. So that's why the problem is occurring.
Thankfully, there is also a very easy fix. Just go to Mesh > Separate Connected Surfaces. When you do this, the software will analyze your mesh and check to see if it is actually made up of multiple parts. In this case it is, so it will break it up into two separate models. Now the software properly knows that there are two models. If you slice at this point, everything works as you would expect (see screenshot).
So moral of the story is that if you encounter an issue like this, it would be good to check the mesh to make sure that you truly have one single water-tight STL file, and not multiple overlapping files in a single mesh. I think some other programs run the Separate Connected Surfaces command automatically every time you import a file, but in S3D you just have to click this yourself if you think that is the problem.