I know that Linux Mint 16 is still just an RC but I think its important to talk about issues that you find, when you find them.
I have an HD 5870.
Installing the proprietary drivers and trying to span my desktop across both monitors causes the following error:
org.gtk.GDBus.UnmappedGError.Quark._gnome_2drr_2derror_2dquark.Code3: required virtual size does not fit available size: requested=(3840, 1080), minimum=(320, 200), maximum=(1920, 1920)
I also noticed that any proprietary driver, including the beta, causes an application I'm running with Wine to flicker. I had the same setup (drivers/wine ) on Ubuntu 13.10 and everything ran fine.
Here is the bug I've posted: