So you took an installed system, you backed up and restored "everything" (including /etc and everything else, which probably means /usr), and the restore screwed up the permissions, meaning didn't restore them. At this point, I would say you have a completely broken system and should reinstall.
I know little about mtree. In theory, it might help to just make everything world readable (and perhaps even world writeable): Start in single-user mode, and do "chmod -R a+rw /". But that would be completely insane, and even if it worked (not sure), you would end up with a completely insecure system which must never be exposed to the network. But also, the permissions and ownership on files are not trivial. You can't simply say thing like "everything under /etc is user=0 group=0 permissions=644", its much more complicated than that. So I don't know where you would get the specification for mtree from.
I suggest reinstalling. And stop doing things that hurt.
