Well, any tool or process in ZBrush that redraws topology (Dynamesh, live Boolean, Sculptris Pro, Knife brushes, etc) has the potential to introduce errors like these. Sometimes users can attempt to fuse geometry in some pretty ambitious ways and this can result in some problematic connections being made. This is why it’s important to check your mesh for errors with Geometry> Mesh Integrity> Check Mesh after any phase of your work where you have been redrawing topology, and before moving onto any phase where you need the topology to remain stable and unchanged.
If you check your mesh and see Mesh integrity warnings in ZBrush, that problem needs to be dealt with. These errors can have differing levels of severity, but any mesh reporting them should not be trusted. It can result in the mesh crashing when you attempt to work with it, or produce odd behavior when used with other features.
For minor errors often times “Fix Mesh” will deal with it. However it is possible that your mesh is fundamentally malformed or problematic in one or more areas, and that the mesh will continue to generate these errors even after “fixing” it. In these cases you need to identify the problem areas, and either redraw the topology in a stable configuration, or cut the area away entirely and resurface it.
Dynamesh in particular can create especially problematic geometry if care is not taken to make sure it is a closed volume and that every area of the mesh has a sufficient degree of thickness. If Dynamesh reads a volume as open or 2D, or a section does not have sufficient thickness, the geometry in that area may begin to disintegrate after a Dynamesh process, leaving floating points or non-contiguous sections of mesh floating in space around the surface. This type of geometry is going to be a problem for many processes in ZBrush even if it is not reporting errors. Sections of geometry like this are prime candidates for cutting away and resurfacing when you have a mesh that keeps reporting issues.
In the case of fusing a bunch of tiny rings to the surface of another mesh, this will almost certainly produce complicated geometry with a lot of tiny overhangs, undercuts, and negative spaces that would be problematic for a 3D printing process if you export it directly. It could also result in geometry that is problematic for ZBrush. For best results in ZBrush and 3D print, you want to be working towards clean, closed, watertight volumes. For your purposes here I do recommend resurfacing your mesh into a clean watertight solid that reports no errors, and re-projecting the geometry from your original mesh as surface detail.
Now, if no errors are reported in ZBrush and ZBrush reports that the mesh is watertight, I might be skeptical of any minor issues the slicing software reports. These programs can be overly fussy, and I personally never experienced a mesh that would not print as expected if it reports as sound coming out of ZBrush. However, your experience may vary.
