Syncing OS X Notes with iCloud I can sync notes when I am connected directly to the internet but not via our corporate lan.

Our network has http/https open but most other ports are blocked.

Which ports does the OS X Notes app use for syncing so that I can request for them to be opened?
Notes in Mac OS and iOS are still based on IMAP email. When you try to set up iCloud notes sync for the first time without having an iCloud email address, you’re forced to create one. I had this experience at last in Mac OS 10.8.4.

Ask your IT staff to open ports for IMAP email which are usually 25, 143, 587, 993.
Hope that helps.