Posts by unregistered users that are added to theads on a delayed basis do not show up in the 'New Posts' list. Is it possible to change it so that they do?
It likely isn't possible, without hacking the posts so that the timestamp of submitting the past becomes the timestamp of when the post was approved (since New Posts works off of time since you last logged in). One alternative, though, would be to decide that the forums now have enough steam to say that people need to register to participate. This would clear up 70% of these instances, but there'd still likely be the people who don't confirm their email addresses (and are therefore moderated).
The fact that unregistered posts can be overlooked in this way is another reason why users should register if they want to ensure their posts are read. Unless much of your time is taken up by moderation of these posts then I would say keep things as they are. Another alternative: The moderator can follow up an unregistered post with an automated/scripted 'bump' to bring the thread to the top. The 'bump' message could be something like "Accepted post from an unregistered user."