I realized, after hanging up with the first Apple support rep, that his explanation didn't quite make sense. I was accessing the iCloud service in a very modern web browser, so the operating system (OS X 10.6.8 or even a non-Mac) should not have the kind of problem I was experiencing. So, I made a second call to Apple Care, described the situation and the previous rep's explanation, enabled Screen Sharing, and duplicated the error using multiple browsers and multiple iCloud accounts. After creating a bug ticket, I was transferred to a senior level tech. After 55 minutes I'm still on the phone with Apple Care, so I don't have a solution for you yet (sorry), but I will post it if I am ever made aware of it. My guess is it's a bug and Apple will resolve it whenever they feel like it. (Maybe the solution is to contact Apple Care and spend an hour on the phone with them. Add up the hours, maybe it'll get escalated.)
For the record, the changes ARE being saved correctly and synchronizing with my iOS devices without fail. The only real problem here is the fact that an error message pops up.
![User uploaded file]()

(It's almost like the system thinks I'm double-clicking the submission, but I definitely am not doing that.) Anyhow the error message doesn't pop up every time, and it doesn't seem to matter whether the contact is a new one added today or an old one from a year ago. It also doesn't seem to matter if I using Firefox or Safari. Unfortunately the Apple Care rep wasn't able to duplicate it in her Safari browser, but she was using the latest version Mac OS X
(Mavericks).