As far as I know you'll need a @me.com or @icloud.com account in order to have Notes sync between OS X and iOS. If you do, read the next paragraph.
I would actually do the following. First go to the OS X System Preferences iCloud control panel and uncheck the Notes synch checkmark. Then go to your iOS device settings app and do the same there under the iOS iCloud control panel.
When you are finished, go ahead in OS X and re-enable the iCloud notes sync in OS X Mountain Lion and then repeat the same process in your iOS devices.
Let me know how this works for you...