Ok. I see what you mean. I'd never tried to move an email from a folder in one account to another before, so I gave it a try. I can successfully move emails from my iCloud to my Yahoo account inboxes, but not to my Google account (which is set up as an Exchange account). I can move an email from the Google inbox to either of the other two.
From this I conclude that you can only move to an IMAP account, but probably from any account type. Though I never actually tested a POP account it is by far the most limited, and unlikely let you move email to an inbox.
Since I never tried this with iOS 4, I can't verify that it's the iOS update itself that changed this. So, my recommendation is:
First, try the usual fixes listed below, if you haven't already done so.
If both accounts are IMAP, then delete and re-add the accounts. This often fixes minor problems.
And if nothing else does the job, well, all I can do is point out that you can still forward your email to the other account. Sorry.
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When you have problems with an app it's a good idea to close it.
Close: With the problem app closed, double tap on the Home button to get the multitask bar. Tap and hold on any icon in the bar until they jiggle, then tap the minus sign on the problem app. This will remove it from RAM and insure a clean start the next time you launch the app.
If that does not work try a restart,
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart.