Same problem here.
I have 3 Macs, 2 with Mountain Lion on and 1 with Lion (can't update 'cause mac is too old).
In Mountain Lion everything works fine, I have my notes synced with ipad, iphone, and two macs.
On my older mac (iMac White 2Ghz Intel Core 2 Duo), all my notes are shown in mail.
When I select them and move them to the Note folder, they keep coming back. Also, everything singel content that is modified in a note, makes the note appear in my mailbox.
This is very anoying.
I tried to install Mail 6.2, but that's not possible, as 6.2 only works with mountain lion.
is this Apple being a bad *** and forcing people to buy a new computer by hassling them with these kind of sh*t?
or is this a solution for this matter?
think different?