I have been playing Diablo III since shortly after it was released with only a few minor problems, mostly caused by Blizzard updates.
I have a GeForce GTX 465 and nvidia-304 driver.
Only thing I would suggest is make sure you are using the correct and updated nvidia driver. I also think it is suggested you run winecfg and set Diablo III.exe to run in Windows 7 environment.
[~]$ dpkg -l|grep nvidia-
ii nvidia-304-updates 304.108-0ubuntu1 amd64 NVIDIA binary Xorg driver, kernel module and VDPAU library
ii nvidia-common 1:0.2.83 amd64 transitional package for ubuntu-drivers-common
rc nvidia-current 295.40-0ubuntu1 amd64 NVIDIA binary Xorg driver, kernel module and VDPAU library
ii nvidia-current-updates 304.108-0ubuntu1 amd64 Transitional package for nvidia-current-updates
rc nvidia-settings 295.33-0ubuntu1 amd64 Tool of configuring the NVIDIA graphics driver
ii nvidia-settings-304-updates 304.88-0ubuntu2 amd64 Tool for configuring the NVIDIA graphics driver
rc nvidia-settings-updates 304.88-0ubuntu0.2 amd64 Tool for configuring the NVIDIA graphics driver
I have winecfg set to run Diablo III.exe with these graphics settings checked
Allow the window manager to decorate the windows
Allow the window manager to control the windows