Looks like an update is out.
http://sites.amd.com/us/game/downloads/Pages/crossfirex-app-profiles.aspx

Area of interest: - World of Warcraft DX11 version CrossFire update

If you don't remember how to enable DirectX 11 mode:

Right-click on the shortcut you use to start WoW and select "Properties"

You should see a target line in the new window that is already highlighted.

Add -d3d11 to the end of what is already there, be sure that there is a space between the hyphen and the end-quote and that there is a space.

It should look similar to this:
"C:\Program Files\World of Warcraft\Launcher.exe" -d3d11

Try the game again afterwards.

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Q u o t e:
I believe the alt-tabbing is an ATi issue and not Blizzard's since I have the same effect in Civ5 when I tab out.

Also, my reflections in DX11 still don't work. I'm sure it's a known issue, but it's a bit bothersome. Dual 5870s if it matters.

On a semi-related note Viewport addons completely destroy the new water and sun effects in either dx9 or 11. I like maximizing my play space and not having it cluttered by addons, so if Blizz could allow these types of addons to adjust how the water and sun stuff is displayed, that'd be awesome.

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Viewport fix is in the works and will be in a future patch.

Basic reflection or specific reflection? I have a single 5830 and reflection seems to work, but no character reflection.

Developers can reproduce the slow alt+tabness in general as well as where the image may stick on the desktop/screen after being alt+tabbed. It does not seem to be vendor specific.