Having this problem as well. Gallery field 1.1.0, WP 3.8. Two of my admin users can edit captions / titles on images, but my editors can’t. Tried upgrading the editor to be an admin, but still only shows “Drag files here to upload.” Even tried creating a new admin account entirely but it has the same issue.
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users