Apple Mail problems - duplicates of messages

I am having a problem with two of my Mac users at work

On the one machine it keeps making duplicates of messages in the inbox for the last month. It is setup as a POP account. So I deleted the messages, and then also deleted the messages off the server in case it was trying to pull the messages again, and didn't realise it had a copy of the message already. After a couple of days, it pulled about a hundred messages that it had already pulled, and were marked as unread. I even ran a virus scan with ClamAvX, but this did not pick anything. Anyone else had a problem like this? If so, how did you resolve it?

On my other Mac machine. The client has a Macbook with an IMAP account setup. When the user is in the office, the mail works fine. But when the user is at home, and they send mail, for some strange reasons it will send out the message twice. Any reason for this?

Thanks in advance for any assistance.