I wonder if this is related to
1. Open a course.
2. Turn on editing.
3. Navigate to a topic section containing multiple items (files or activities, does not matter). Make sure that the section is hidden.
4. Click the Edit menu and attempt to select "Delete" from the menu.
Any menu options that are overlap the topic section below the current one will be inaccessible.
You can see an example (video) of it here: http://www.screencast.com/t/qdjjlVTpTQb
It seems as though the menu items are set behind the topic section below. Once the section above is unhidden the complete edit menu (and delete option) are accessible.
This only affects the items for which the edit menu overlaps the section below.