I think it would be a really nice feature for moderators to have a feed showing all new posts & topics (perhaps split into separate feeds) in order of creation (newest first). Displaying the full content of each entry like the review queue (unlike the public facing new topics filter).
This would make it easier to keep an overall eye on the latest posts and topics to check for content that does not comply with the rules. Allowing moderation actions to be taken directly from the feed.
I think this could significantly decrease the burden of moderation for active forums of all sizes. Particularly for monitoring new replies/posts (as opposed to new topics).
It would be a quick and efficient way to see all the new content without needing to navigate through a lot of threads to check the latest posts. Meaning that there would be less chance of non-compliant posts being overlooked while also being significantly faster, easier and efficient.