One of the worst problems with tagging is the tendency to
create multiple tags that are slightly similar, or to create tags
with typos. Offering some kind of auto-complete feature would help
avoid this. If I have a tag #cars already, I will be less likely to
accidentally create a new tag #car if it offers #cars as an
# key on the iOS shortcut bar
It would help facilitate tag entry on iOS if there was a #
symbol on the shortcut bar.
An "untagged" tag - Very useful, exactly as Luhmann has described. Apple Notes.app has the 'Notes' folder which serves this purpose. Every now again I go through them, and Notes I want to sort go into a folder. (In Bear's case, I would go through and tag them.)
Auto-complete - exactly as described.. I don't want to accidentally create similar tags. Evernote has tag autocomplete, it makes it very easy.