Notes 10x Duplication (Without iCloud)
Try to close Notes  and delete ~/Library/Containers/com.apple.Notes/Data/Library/Preferences/com.apple.Notes.plist.

Relaunch Notes to see if the same problem exits.

Update

This method suggested will remove all your local Notes and resync with the notes stored in iCloud. Just for record:


Open your favorite Terminal. (If that sounded weird, just open /Applications/Utilities/Terminal.app)
Quit Notes.app.
Enter rm -rf ~/Library/Containers/com.apple.Notes. and press Enter.