If you have users that need access to the "publishing list manager" you have to make them an Admin. Would be great to have "publishing list manager"-access as a user permission.
I second this. It would perfectly fit in the tools section of the access rights dialogue.
addition: allow non-admins to use publishing lists that are already created.
Both suggestions are great (allowing non-admin users to use existing publishing lists, and adding the publishing list manager to the admin section). Publishing lists can be huge time savers and it's a shame that only admins can take advantage of them.