Talking about GNOME
I think if you want innovation and strong improvements (instead of a few tiny steps now and then), you should think outside of the scope of some desktop environment.
Integration with more or less popular web services is not good enough if you want software freedom. I’m specifically thinking about lock-in. Of course free-software based web services wouldn’t be good enough if they don’t become popular 😉
I wonder if web services could run in a distributed fashion, somewhat similar to bittorrent. I’d expect some hard problems, especially regarding security.
Running web apps on the desktop is likely to be a huge step backwards in the quality of interaction. There should be a framework for running the same applications locally or on a (virtual) server.
It should become much easier to deal with having your data spread across several devices and locations. For example 2 desktops, 1 at home and 1 at work, a laptop, a handheld and a web service for backup. For this I think there should be logging of where files came from and where they have been send / copied to. Combined with versioning. Oh, and closed, specific solutions for organizing photos and music don’t cut it. It should be the same means for all files, everywhere.
What else? Multi-touch with fully customizable gestures. A canvas to draw everything on, no canvas widgets. An authoring environment for said canvas, a bit like Flash. Persistence instead of having to save manually …