I've noticed that under the username, there's "Show unread posts since last visit" and "Show new replies to your post" links...
However, some members may not have noticed it at all; I've only noticed it a minute ago...

Could an admin perhaps add buttons to the user bar below that...?

Okay, it's done.
The names are a bit lengthy, though it's better that way, in my opinion.
That way, better to know what it does; just using "Unread Posts" could mean all unread posts on the forums.

Thank you, KarjamP.