I have the same issue.
I called apple support and after wasting an hour and a half on english lessons with the lovely, but helpless lady on the phone I have done some experimentation and I believe I have identified the issue:
Notes is broken - there are now two versions of the notes data:
1. One for the account you are logged into as your primary account, and that should synchronise with all other devices logged in with the same primary account. 2. The other is for any devices logged in with an appleID as one of the Secondary Accounts. This will sync - but only with other devices using it as a secondary Account.
So - in a hypothetical family where there is Dad, Mum and Child - each of whom have, for instance, a Computer running El Capitan, an iPad and an iPhone both running 9.1 the following will occur:
Dad updates or creates a note on his account on one of the devices which have him logged into "Dad" as his primary account - he will see this on all his devices but no one else will see the update as they will have Dad as one of their secondary accounts.
Dad updates or creates a note on Mum's notes on one of Dad's devices. He is logged into Mum as a secondary account. Dad and Child will be able to see this update/new note as their secondary accounts will synch, but Mum won't see this as it was not made on her primary account, nor will she see Dad's update from above, as that was done on Dad's primary account, and she is logged in as a secondary account.
Child will only see a note updated on Mum's account that Dad did, or a note updated on Dad's account that Mum did (as these were both secondary accounts and all secondary accounts sync with each other - but Child will not see anything that anyone else does on their Primary Account (as they are logged in as Child as their primary account.
This is clearly nuts - but I couldn't get this message through the lady on the phone nor to Apple - who seem to make it very hard to provide feedback or bugs these days. Their best advice was to delete the accounts and re-sync which a) didn't work and b) took forever to re-synchronise the mail account.
BAD APPLE - not that they listen to these forums - where we understand their software better than they do, it would appear.
Sorry that this is not a fix - which would require some Quality Control at Apple.
It only seems to be an issue if you have multiple accounts (e.g. a family) and that you log into yourself for your devices, as do the rest of the family - which ironically is precisely what apple suggest that you do...
Apple is becoming more like Microsoft every day - the focus is on selling you iTunes and other material, not making their software "just work" like they used to be before Steve Jobs left. RIP (although I fear he would be turning in his grave)
C&K
