node/add page shows 2 of every type. How do I fix this?
I've fixed it.

The problem was that the table menu_links had duplicates in it for the content types.  How they got there, I have no idea.

The fix is to find the menu_links table using phpMyAdmin and search for the links there were duplicates of (title link_field using LIKE %...% operator). Then simply, drop them from the table.  The reason is because the node/add page is just a page (or Overlay) view of the items in the "Add content" menu.