Does selecting "kde3" at the kdm login work? If it does but "default" doesn't that points to you having a $USER/.xsession file that kdm is executing. "default" exists to allow the user to run their .xsession file if present otherwise it falls back to the default.
KDM does work properly in sid with KDE 3.1.2, I just uploaded the kdebase 3.1.2 debs today. Chris