For any OS, what I think would be truely innovative would be as much as possible hardware agnostic system. . . I know its been said before enough times, but still I think somebody needs to really take it to the next level be it Linux, Amiga, MS, or Apple. Make your software run unchanged on anything and I am sure people will flock to it. . . and at the same time give them the right to run it on whatever they own.
The next idea I think would be great to have implemented (at least from MS's point of view) would be to make all of their software (Media Player, Office, a paint tool thats not paint, Windows Movie Maker etc...) extensions to the system. For example, I open a jpeg in the viewer. If while I am looking at it I decide I want to work on it a bit, I simply go to the file menu and choose something like "Change to editor", and the very same window instantly gets editing controls added to it, maybe top/side rulers, etc... when I am done, I can save it and just as easily close it as select "Return to viewer" or something. Every program could be accessed this way, instead of launching multiple programs to work on files, you simply change to the appropriate mode for editing or viewing of any file type directly. 3rd party apps could be extensible the same way. For example, instead of Photoshop being a program itself, it just integrates its controls/plugins/filters/etc into Windows and when you choose to edit a picture they are available to you.
There are other simple things that MS could change in Windows to make it more comfortable for me. I detest having the same File, Edit, View, etc. . . menus in every friggin window. Why not just make it available with a right mouse button click context menu that is already there? As well as put it at the top of the screen. . . but doesn't Amiga (or Gateway) hold the patent on changing a screen title bar to a menu system with the right mouse button? At any rate, most people I know love their screen / window space and repeating the same information in every window is just a waste.
There are many many other things I would like changed (or changable) in Windows, but I won't go any further here. Aside for trying some radically different approach to UI layout that will likely scare novice users I don't think any OS has anything "unique" or "innovative" to offer anymore.