Normally there's no way that section 0 can become invisible in a course, but for some reason it did (for a few of our courses). I think it had to do with some import/export thing, but that's another issue. However, when section 0 does become invisible, it's very confusing.
1. It still shows up completely (so you don't realize it's invisible).
2. There's no way to change visibility without mucking with the database.
3. Visible modules in the section will display, however, as soon as they're set to invisible, they can't be set to visible again.