Notes iCloud sync fail Yosemite and IOS8
It's a bit difficult to diagnose this with the info you've given but from experience I've found that you are able to reliably "force an sync" with any sort of iCloud data by going to System Preferences and signing out + signing back in (it'll warn you about removing iCloud data from the device, etc.) 

As said in the previous answer, make sure you are syncing your notes with iCloud and not with a) another provider (Google, Exchange) or b) not syncing at all (i.e., storing locally). Verify this on the iPhone in Settings > Notes > Accounts or on the Mac with System Preferences > Internet Accounts.

The best way to see what is actually being stored in iCloud is at its web app like you've been doing.