Recently I have revisited my original approximation to a definition of "weak ω-category" (as a simplicial set with extra structure) trying to remember some of the things I have thought of since those days. The main thing I want to report is a method of constructing the thin elements from the mere simplicial set so that being a weak ω-category becomes a property of a simplicial set rather than involving extra structure. I have many conjectures.
For more details, see my preprint of the same title.