I noticed a lot of mesh errors in the original wireframe skull, so I went back to the source and rebuilt the skull with a much cleaner mesh.

I also scaled it up to make it print a good size, you can scale it however you want in your slicer.

I created the base and added it on too, so it'll adhere and print easier and provide a nice base for whatever you put inside.

The print in the image was printed at 150%, 0.2mm layer height in silver PLA.

This model has been verified as manifold in Rhinoceros 3D, there are no gaps or errors in the mesh that I can find.

If you have errors and holes in your slicer, it is probably an issue with the slicer getting confused with the complex detailed geometry and/or some settings that need to be tweaked to take into account the small geometry.
Alternatively, printing in a larger size can help too.

THE MESH IS MANIFOLD AND HAS NO HOLES! If your slicer is showing holes, it is a settings or slicer issue due to the complex detailed geometry. I suggest you double and triple check settings and/or scale up to a larger size. This is especially true around the nose and eyes.

[EDIT 2019-07-22]
I have completely cleaned up the mesh, it now has no overlapping faces or open gaps anywhere.
This is about as perfect as it gets now.

[EDIT 2019-07-20]
I fixed the base and simplified it a lot (the boolean union to add the base to the skull was borked) so it should print much better now.

I've supplied STL and the original Blender files so you can remix and stuff if needed. Just be cool and somehow credit me, philnelson, and of course garygeo for the original base skull model. :)