If the account is IMAP, and the IMAP server supports tags, then tagging on one computer makes the tag appear on other computers with the same account and the same set of tags. If that's not possible, other options are to move the message to an IMAP folder named, e.g., Read by X. There are also add-ons to edit the Subject or any part of the message.

Unfortunately it is a pop account, so does anyone else know of any other add-ons that could work?

Pop account emails remain stored on server only if each pop mail account is set to leave a copy of message on server. Each subsequent download is independent and only stored on the computer to which it is downloaded. This means anything you do, eg: tag, delete, change subject etc is only done on your computer. It is type of one way system, you cannot effect anything stored on server other than delete, so it is in an unaltered state for another person to download. Pop account folders do not synchronise with server.

This is why there are imap mail accounts to store emails on server and allow imap account access as a sort of virtual view of what is on server by synchronising folders.

I suppose another way would be to use shared folders for the profile folder name, but then there may be restrictions on only one person having access to one Inbox mbox file at one point in time. It's not exactly ideal, but works for some people. http://kb.mozillazine.org/Thunderbird_:_FAQs_:_Network_Access#Multiple_PCs

You could forward a read email to your pop email address - like sending to yourself saying X read this in the Subject, but that might unacceptably increase your sending/receiving quotas.