I prefer a popup in view and visualeditor mode (maybe anything similar in source editor too), that can be opened by clicking on a button next to the entry (for example, similar to references, a [Data] link). In this popup, you can change and delete it or add, change and delete its references. Maybe some more functions can be added, for instance (just ideas):

• If a statement with references is deleted by popup, it isn't deleted, but ranked as deprecated (maybe with override possibilities)
• In general, a better GUI for refernces where the tool asks for the type of reference (book, web, ...) and adds the appropiate properties automatically
• A show more link to edit more of the item, at least the identifiers and statements of the same property (the count of statements with this property should be listes without clicking show more), here it would be useful to be able to add statements (useful for lists)

A further idea would be to make descriptions editable from Wikipedia apps, where they are shown (I think quite easy).
I think this would make Wikidata way more usable for common Wiki editors.

There are already partially functional gadgets on the French and the Russian Wikipedias.

There's a design prototype on wiki: https://m.wikidata.org/wiki/Wikidata:Client_editing_prototype

(This was discussed in WMTC18. See some notes in image 6 in T206085#4696219)

Update: we are working on this under the umbrella of the Wikidata Bridge project.