I have the same problem when running the provided installation script. There seems to be a problem using wine 1.3.7 during the installation. You can find the latest installation script that was ran by POL at ~/.PlayOnLinux/install. You can edit this file and later run with POL using the tool "Run a local script". By commenting out the following line your system default version of wine will be used during the installation.
#Use_WineVersion "$WORKING_WINE_VERSION" (line 54)
This solved the installation halt for me. Be aware, on my system the background image was not rendered during the installation, but present. So it seems like you desktop is not responding anymore, but when you switch to a different desktop all buttons will work again. This was due to the installed version of wine on my system being 1.0.1 (Debian is falling behind). You could also try changing the wine version by changing the line: WORKING_WINE_VERSION="1.3.7"
Edited by rawnar
AMD Athlon X2 3800+(@3.0GHz), 6GB DDR2-SDRAM, Nvidia Geforce 8800 GTS 512(2x), Asus Xonar D1, Debian Squeeze AMD64.