I'm going to suggest possible solutions that are merely trial and error. I am no expert in the matter, so take caution when implementing any of my suggestions.
First, I would like to suggest doing the following command:
sudo apt-get install ia32-libs
This should pull in some 32-bit libraries; perhaps the one you need? If this works, hooray! Don't touch anything else.
If that didn't work, completely remove the AMD proprietary drivers. I have no idea how you installed them, but this link is fairly sufficient: http://wiki.cchtml.com/index.php/Ubuntu_Precise_Installation_Guide#Removing_Catalyst.2Ffglrx
sudo sh /usr/share/ati/fglrx-uninstall.sh
sudo apt-get remove --purge fglrx fglrx_* fglrx-amdcccle* fglrx-dev*
sudo apt-get remove --purge xserver-xorg-video-ati xserver-xorg-video-radeon
sudo apt-get install xserver-xorg-video-ati
sudo apt-get install --reinstall libgl1-mesa-glx libgl1-mesa-dri xserver-xorg-core
sudo mv /etc/X11/xorg.conf /etc/X11/xorg.conf.backup
sudo rm -rf /etc/ati
If the fifth command doesn't work, replace with:
sudo apt-get install --reinstall libgl1-mesa-glx:i386 libgl1-mesa-glx:amd64 libgl1-mesa-dri:i386 libgl1-mesa-dri:amd64 xserver-xorg-core
Then reinstall your proprietary driver. In 12.04, open the dash and open the "Additional Drivers" application (or alternatively, run "jockey-gtk" from the command line). Install the latest driver from that program (fglrx-updates). You will NOT get the latest and greatest driver, but you WILL get a driver that has been tested by Canonical and just works. You could get newer drivers (the link I've provided is able to show you one such method. You could also use an x-swat or xorg-edgers PPA, but they're beyond the scope of this question).
One tip, though: Don't mess with graphics drivers. A clean install has the best possible set-up for graphics in most of the cases. Drivers downloaded from websites are always shaky unless you know what you're doing. Drivers from PPAs are generally unstable. The only drivers you should really be using are the drivers Ubuntu ships with (i.e., the open source ones) or the ones downloadable through the "Additional Drivers" program.
I do not know whether the fault of PlayOnLinux lies in a bad driver set-up, but I personally think that's the culprit.
One last thing, since you're using an AMD APU:
sudo apt-get install amd64-microcode
This nifty little package solves a lot of problems with AMD APUs.