Been using Linux as my OS of choice on home computers for a while now. The desktop experience has come a long way to achieving what I would consider "expectation parity" with a few exceptions.
The biggest thing I hope to see change is Apple start publishing iTunes for Linux. That's not because I use it, but because many people who otherwise have no reasonable need to use Windows would be able to switch to Linux.
In a similar vein, I hope to see WINE get to the point that pretty much any random Windows based application just works so that migrating people is SUPER easy.
Lastly, and I'm sure this will ruffle some feathers, I hope Canonical gets convergence working properly across form factors so that for someone that wishes, they could turn their phone into their single computing device and not give up having access to a standard desktop in the process. If ever Linux were going to "win the desktop", this might be the best bet.