If I mistakenly delete or otherwise mess up a Note that is stored in iCloud, is there a way to restore a past version of the Note?
Short answer is no :(. That is, unless you can get to the note before iCloud updates it, but that would not be much time at all.
Not that they are in the same class, but one can do that with Time Machine. It allows one to go back through, and it has saved and kept track of the changes that have been made to documents.