A question that is a duplicate of another question, in terms of appearance, should be treated the same as any other question. If there's something that needs to be fixed, fix it. If there's nothing broken, leave it be. Being marked as a duplicate does not, in itself, change the original content of the post. So treat them like you would any other question.
If the question is already closed, then there is really nothing to worry about. It won't attract answers, after all. For open duplicates, it'll be treated the same as any other open duplicate - no matter how obvious a duplicate is, if not enough people agree and it doesn't get closed, that's that. That's why closing is a community process in the first place. Sometimes, in fact, bringing a very old open duplicate to the surface may attract the votes necessary to close it. In the end, the important thing is that you shouldn't let the closed, duplicate, or other similar status of a question influence the necessity of an edit. Though do make sure you don't edit out the duplicate link, if there is one.
For migrated questions that are missing tags, there is never a good reason to leave something mistagged. Tagging is a matter of categorization, unlike the question body which is a matter of content. If you can fix tags to apply to the actual content, it's highly recommended to do so. I would traditionally prioritize these, and basically tend to other editing duties like fixing 'stackoverflow' to "Stack Overflow" when coupled with fixing tags.
There's a post somewhere about how much you should be thinking about fixing when deciding to edit very old posts, but I can't find it right now, but basically if the changes are very tiny or few, it may be wiser just to leave it be. But if there's some problem in tagging, there is a definite positive to fixing that no matter the age of the post, so while you're fixing that you may as well get your edit fix in.