I have only run into one issue on my new iPhone 4S, when trying to delete email on an IMAP email account I get the “unable to move message” error. Here is how I solved this problem.
To cure your “Unable to move Message” on your iOS 5 device follow the following steps:
Settings → Mail → click on the offending email account → click on account → advanced → deleted mailbox → then touch the Trash icon “on the server”
Note that these directions are for IMAP servers. They should work for POP3 email accounts also, however instead of choosing the server based trash, chose the trash folder on your phone.