Late last year an update to the Battle.net game launcher exposed a bug in in the Mesa library. This caused the launcher to look something like this while running under Wine on Ubuntu 14.04 with some graphics cards:
You can find the opened and closed bug report here. Sadly this patch has yet to make its way into the default Ubuntu 14.04 repositories (and who knows if it ever will) so to resolve the issue you need to update your Mesa packages. You can do this via the Xorg Edgers PPA with the following commands:
sudo add-apt-repository ppa:xorg-edgers/ppa
sudo apt-get update
sudo apt-get dist-upgrade
You might need to restart your X server for the changes to take effect. This fix should work with all Wine variants such as Play on Linux and Crossover. If you are using a non-Ubuntu based distro, you will want to install Mesa version 10.4 or newer. Enjoy your gaming!