Neither the native client nor Web Access supports drag and drop between the local session and the remote one (or vice versa). This can be annoying for many workflows where you instead have to use the clipboard or some other mechanism. E.g. dragging a link from a local browser to a remote application in order to get the URL there.
It would be cool to be able to drag-and-drop files as well. Apparently, Microsoft's RDP app can do that?