FYI I just figured out how at least some of my note duplication was occurring.
This morning I opened notes on my phone and I had a note open, it was something I'd been working on and had edited on the computer just a little while ago. When I closed the note, it was there TWICE. It appears that if you have a note open on your iPhone, and edit it on your computer, it splits them and saves both separately.
This kinda makes sense because if there are unsaved changes in one place you don't want them to be lost by the other updating. But it's my experience they sync in a second or two if they have a network connection. My computer and phone were both online 100% of the time. I think the problem is it can't update a note if you have it open. I've seen my note list change almost immediately when I add or rename a note on another device, but I've never seen the content change on one that I had open.
I work for the Department of Redundancy Department