If I have a note with several checklist items (some with a #due tag), the #due tag should be deleted or renamed to #done after check/complete.
I think that would be too invasive. The app shouldn’t really be editing your text. The way we envisage it, you just remove the tag when you are done.
Perhaps at some point we can add more integrated due dates, rather than just tags, and at that point, it would automatically update, because it would belong to the item rather than just the text.