With the November update, Open Whisper Systems (OWS) introduced an "advisory mode" setting that allowed users to be notified of a safety number change but not be prevented from exchanging messages. After testing out that setting and collecting feedback from users, OWS has made some adjustments to it, which are now available for testing in the beta channels of the Signal app.
In advisory mode, if you receive a message in a conversation with a new safety number, a notification will appear telling you about the new number. And it will stay on the screen until you see it. Even if you get a few new messages, they won't push the notification off of the screen. When sending a message after a safety number change, the same notification will appear and you'll be able to send messages as long as you've had the chance to see the notification. If it happens to appear just after you send a message or just before, the message won't be delivered until you approve it. Users can also now mark a safety number as "verified" and any safety number changes from a verified conversation will require manual approval even if you've switched on the advisory mode.
The changes are available in beta now and OWS encourages users to send along any feedback they have.