I use the Mix'n'Match search feature extremely frequently when editing Wikidata. It works very well when you want to complete all potential authority control properties for an item (mostly a person, but can be a concept or a geographical feature or a building too, for instance).

I'm not a coder but I have a hunch that it could be quite easy to create a gadget that adds a link to the Mix'n'Match search for the current item to the toolbar on the left.
The gadget could use the English label of the item as search string, with fallback to the label in another language where a label *is* present. (I know this is not perfect, but it would work in many cases.)

An example:
Item https://www.wikidata.org/wiki/Q2351102 is the Belgian artist Leo Copers. Has "Leo Copers" as English label.
Permalink for search for his name in Mix'n'Match is http://tools.wmflabs.org/mix-n-match/?mode=search&query=Leo%20Copers&exclude=&include=
The gadget could link to this permalink URL. With one click I can then take a look and complete the item's authority statements/matches.