While downloading the free, for private use, edition of Teamviewer for Linux, I found this How do I install TeamViewer on my Linux distribution? where in the section for Debian, Mint, Ubuntu, Kubuntu, Xubuntu… I found a simple way for the installation of 32bit packages on 64bit Debian.
For the 32-bit package:
sudo dpkg -i teamviewer_linux.deb
In case “dpkg” indicates missing dependencies, complete the installation by executing the following command:
sudo apt-get install -f
For this to work, of course, you need multiarch-support.
In the same page is also explained why the 64bit precompiled packages, cannot be installed on multiarch systems.
Notes to Multiarch:
On newer 64-bit DEB-systems with Multiarch-support (Debian 7) teamviewer_linux_x64.deb cannot be installed because the package ia32-libs is not available anymore on these systems. In this case you can use teamviewer_linux.deb instead.
In case you get the error “wrong architecture i386” you have to execute the following command lines:
dpkg --add-architecture i386
For further information: http://wiki.debian.org/Multiarch/HOWTO