It gets weirder. I have both documents open and am editing both. One is now displaying the heading numbers in the nav pane in full. The other is not. As far as I can tell there are no relevant differences in options settings. Just to top it off, the nav pane in one window sometimes shows the headings from the other document.

In fact, taking a second look--one document's headings are displaying correctly in its nav pane, and for the other document, some are and some aren't.

UPDATE: Fixed it!
The heading styles in both documents are the same and are pretty tightly controlled--both documents were created from the same custom template and one originated as a copy of the other. I accidentally discovered that selecting a heading and pressing Ctri-Space fixed the problem for one heading--evidently there was some sort of character format issue (too subtle to be obvious on the screen) involved. But even odder was that after I fixed a few headings like this, the problem disappeared for all of them.
Thoughts?