To replicate:
1. Create two objects
2. Apply same effect two both, for example Bumpmapping
3. Put them in the same family
4. Go to event sheet editor, create a new action for family
5. Try to change Bumpmapping light intensity or any other value.
You should get a "There are no parameters available for the selected item". You can press finish, but the resulting action doesn't do anything the value can't be changed.
I would consider this as a quite severe bug.
Davo, this one's for you. Looks like family effects don't retrieve parameters properly.