Could be done, but, it's not as simple as it seems. There will probably be forum threads that some people are totally uninterested in, or that one thread that keeps getting replies.
The new post icon would be constantly visible.
You'd need some mechanism to mute threads, or only show replies to threads you've posted on, etc.
The basic "there is a new post in entire forum" thing is possible, we actually do it on guild forums. If you see your guild profile breadcrumb bar, it'll let you know if there's a new post there.
Quote from Shoebob
Can we get a New forum post Icon up by the Turns per hour or a Notification a new post has been published. That would be neat
