After investigation and some debugging, I found a potential cause and so googling it returned me this:
"We have investigated this issue and determined that it is caused by the video card hardware/drivers missing certain features of OpenGL 2.0 that are required for Google video chat on Linux. We are working to support these kinds of video cards, but in the meantime the following work-arounds may allow you to place video calls:
For users of ATI hardware with the open-source drivers: Try EITHER switching to the proprietary ATI drivers (which should offer full OpenGL 2.0) OR continue to use the open-source drivers and create a file at /opt/google/talkplugin/envvars with the content "LIBGL_ALWAYS_SOFTWARE=1" (which will disable hardware acceleration, but incur a performance penalty)
For users of older-model NVIDIA hardware (e.g. GeForce4): Try uninstalling the NVIDIA drivers"
I am using the FOSS ATI driver... I am currently trying the mini-hack fix.
EDIT: The fix works
# echo "LIBGL_ALWAYS_SOFTWARE=1" > /opt/google/talkplugin/envvars