I have just implemented a latest posts feed, after several topics of people asking for it!
It will return the posts with the last 50 ids, in order, with posts you can’t see filtered out. You can attach a ?before=5678 to only see post IDs 5629 thru 5678. With that scheme, it should be fairly easy to make sure your service sees every post it has access to.
For those of you using an admin api_key and api_username, and plan to display the results of this, you should probably use a non-privileged account to hit this endpoint, or your Staff-category topics and private messages are going to be displayed.