We had a complaint from our QA people that the "edit tag" link was only available from tags on your user profile, not for other sorts of tags. This is more visible because we've got the course tagging installed already.
I've given my users the tag:edit capability but not the tag: manage capability, and the code displaying the link does this:
(has_capability('moodle/tag:edit', $systemcontext) && (tag_record_tagged_with('user', $USER->id, $tag_object->name) || has_capability('moodle/tag:manage', $systemcontext))
What I think we need really is a better split between what edit and manage capabilities control. To me it seems reasonable to allow a different set of users in to update the description and related stuff for a tag than you want to give access to the full management interface. Why should a user be able to edit a tag just because they've tagged themselves with it (as opposed to their blog post, or a course).
(PS I know there's another bug in here about improving the management interface, but I thought this probably deserved a separate issue - feel free to merge, or subtask if you think its best!!)