Nice! I'm very bad at bash scripting, but I have some comments/suggestions:
1. mv -f update.tar.gz /mnt-system will replace an existing update version, won't it?
2. I think minirt.gz should be modified to move the update.tar.gz out of /KNOPPIX after updating the persistent store - if it does not already.
3. The critical step, copying a live file system, is tarring. Maybe a note to the user when this is done?
4. This could be implemented with two USB sticks, rather than stick+ live CD. But, also, why couldn't the update file be moved into KNOPPIX by the running system itself?
5. /usr/local/bin is an alternative place for such scripts.