Thanks for the reply. This is what I've tried so far in my trouble-shooting:
  1. It looked like the field in question is called "attributes_required" and I did a search on that field using the developer tools. The field was referenced in 4 Admin files and 2 Catalog files:

    admin/attributes_controller.php
    admin/includes/functions/general.php
    admin/includes/languages/english/attributes_controller.php
    admin/options_values_manager.php
    includes/classes/shopping_cart.php
    includes/functions/functions_lookups.php

  2. I installed a fresh ZenCart in another domain in another directory and compared the files I had with the fresh install. They were identical.
  3. I had previously run some SQL's on the zen_products_attributes table to update some prices, so I figured I'd double-check in phpMyAdmin that nothing got screwed up. The 'attributes_required' field in that table looked good, and the correct fields looked like they had a '1' in them. Also, the Admin UI correctly shows the setting of that field.
Any other trouble-shooting tips or hints on what I could look at?