I'm having the same issue today, not sure when it started though. Tried to add an iTunes card to my account & keeps requesting my password. Get the same thing when trying to view my apple ID. Happening on both iPhone 4 & iPad 2. My apple I'd works fine in iTunes on my computer.
Have you tried re-syncing the iPhone to iTunes on your computer? I haven't tried this yet myself because I'm anywhere near my computer at the moment. Would be interested in finding out if this works.
Yes I sync daily, plus I did a couple soft reboots (was working on a problem in sharing calender with another apple user).
Today all of a sudden find my iphone on my phone is working - wasn't last night and I did nothing different, everything else is still logging in fine. But still getting teh error with find my iphone in Icloud. Talkig to technical support right now, they are now checking with a 2nd level support person. They confirmed it was the same apple ID login and password used other places, and that under the icloud settings you had to have icloud turned on (I had).
So after talking to 2nd level support, I was told there is some icloud problems right now that are intermittent. They know about them and are working on them.
So I will try this again in a day or two to see if it works.
Well it has been several weeks now and it is still not working.
I called support before, their answer was we are having some icloud problems, try it again in a few days.
I called again, pushed them to let the developers know there is a problem and I am not the only one experiecing this. I don't have faith it will get solved or in a timely manner. I really don't think it is my job as a customer to debug this (they wanted me to do that).
My cookies are removed regularly, I reboot regularly.
I am on window and use firefox - but it should work fine on this software. Like I said it worked fine for a year or so, though I don't check it often (every month or two).
Would like to hear from others if it works and their configuation. If the apple developers decide to take a look at it the information might help them.
Yes, I am on the latest ITunes but this is not an itunes issues (it is an icloud and iphone app issue).
I have not tried restoring the iphone, too much time to do this for something that doesn't seem related (again, find my iphone not logging in on icloud is an icloud software issue, not the phone issue).
Oh, the phone app found my iphone was having the same problem originally, then it started working a few days later and worked for a couple of weeks, now it is not working again. Seems there is a real bug going on.