Why don't some widgets work on Cyanogen?
Can you download another home launcher like LauncherPro (I highly recommend it) and see if the widgets also don't work there?  It could be a problem with the launcher you are using (ADW or Launcher2).  Or you could re-flash CM6 with the other launcher than the one you chose.

If these are the official Twitter/Facebook app widgets, then I doubt it is because of HTC Sense no longer being available.

Additionally it sounds like you are running a test build of CM6, so it may be a bug.  Check out their forums to see if anyone else has your problem or to report the issue.