Allow users to move/copy files between different sites and libraries on SharePoint online
Currently you can move/copy a file within a Document Library on SharePoint online, but you cannot move/copy it to another Library within the same site or in another site in the collection. This makes the feature much less useful.
Allow users to browse the whole site collection with libraries with the move/copy function.
also to allow move wiki pages to a different site
After the same thing. Currently to move content you need to download it, then re-upload to a new location. Even copying between Explorer View windows, the data has to be copied by the client. Initiating a background move operation where the data is moved within Office 365 will be much faster.
InfoCloud Mike commented
Even more useful if the copy / moves could handle bulk quantities and sizes of files and folders, somehow - I realise this type of feature could be a threat to performance though - so perhaps some way to execute larger moves in the background when system capacity is available.