There seems to be a problem with the drag and drop functionality when trying to reorder activities on the site home page, in that you cannot drag and drop. This seems to affect various themes (clean, essential, standard) moodle 2.6, 2.7 I haven't checked all versions. And AJAX is enabled as I can drag the blocks around.
1. navigate to site home
2. turn editing on
3. add a couple of activities to page (I used labels)
4. Try and reorder by dragging handle, it seems to you cannot do it.
You can however double click and reorder the activity.