Per user request, it is often important for the editors to be able to add custom edit summary message in addition to the automatically generated one. Yet there doesn't seem to be any way for the wikidata users to add that right before hitting save.
On save link mouse-over, show a drop down, and do not hide it unless user clicks outside of the box. Any entered text should be preserved even if the dropbox is closed. Other save links on the same page would not be affected. For mobile, we may have to have a separate edit box.
The first step should make it easy to implement via Gadgets (e.g. by providing some sort of a pre-save hook) so that a Gadget would 1) handle the mouseovers on save to show the popup, and 2) handle pre-save hook to add an extra summary parameter to the post (and be able to examine parameters are being sent.