If you received mail from the server after deleting it, there is something at the server end. Flagged email, unless you have one of the devices set to delete email from the server would still be on the server. If you are just deleting mail from the inbox and are not deleting from the server, then they are still on the server and if you did have a problem with the email client on the phone, it could every well be a problem with the iPhone email client.
Can you access this mail account via a web interface? If so, I would go on there and clean the inbox to only display those emails you would want. Then go on the phone, delete the mail account. After deleting the account, add it back. When you add it back, the iPhone should download everything still on the server, unless it still shows some identification of the client. That should put you back in business.
POP email is not designed to be accessed from multiple clients. It is more for a single email client. This is how things can get confused when responding from different devices and if settings differ when it comes to deleting mail. Good luck.