I continue to have issues, though different from Joey's opening point: I get a completely white page inside the browser. If I resize that window I get some of the hangout controls but not the video. I get error messages from chromium standard output; I need to restart to get them so I'll post them separately.
I'm running the to-be-released Ubuntu 12.04 with:
ii chromium-browser 17.0.963.83~r127885-0ubuntu1 Chromium browser
ii chromium-browser-l10n 17.0.963.83~r127885-0ubuntu1 chromium-browser language packages
ii chromium-codecs-ffmpeg 17.0.963.83~r127885-0ubuntu1 Free ffmpeg codecs for the Chromium Browser