I rebuilt up my primary desktop system with Gutsy and tried out Compiz with my non-Xinerama multi-head setup. It didn't handle it well and after a few hours of trying to fix it I switched back to plain-old Gnome. I reported my findings as bug #178341. There were many bug reports about most of the problems I experienced but it seemed like there was some fundamental problem that was causing them.
First, no window borders (ie, decorations) were present on windows in the second head. I had to reload the decorator with "gtk-window-decorator --replace" to get them to show up. Windows can be manipulated using mouse + keyboard but it's annoying.
Second, the Quit button on the second head would show an invisible power/logout window. I could cancel it with Esc or log out with Alt-L. Other people who have encountered this one mistakenly thought it was a desktop freeze and killed X.
Third, the long default menu pop-up delay was really irritating but it only was present on the primary head, not the secondary. Setting gtk-menu-popup-delay=0 in ~/.gtkrc.mine didn't have any effect on either one. The excessive delay makes the system seem slow like Vista. Regardless, it should be the same on both heads and this leads me to believe that the config files are not being read properly on the second head.
Fourth, the workspace switcher applet didn't function correctly. If I changed the number of workspaces on the second head it would affect only the primary head. It didn't get along with Compiz either but it's a known limitation. Minor issue but further proof of something being broken within.
Other than some Nautilus errors in .xsession-errors there was nothing useful in the logs.
I may have to wait until Hardy for Compiz to be usable on my system. It wasn't an easy decision for the Ubuntu dev team to include Compiz because of the known issues with drivers and stability but it will mean more stability for the Hardy LTS (5-year support) version. The problems I encountered are hopefully specific to multi-head setups as they are not typical for most systems; it would create an unfavourable impression on new users.