After installing the Messages beta, everything seemed fine, but this morning, my iPhone's and iPad's Messages app each had a badge indicating 3 unread messages. After sending and receiving messages all day long, the iPhone still indicates 3 unread messages, but the iPad no longer has a badge. But now my iMac is showing a badge on the Messages icon in the dock indicating a single unread message. I've gone through each of the contacts in the app on each of the devices, but found no such unread messages on any of them.
What gives? Any ideas about how to clear the badges?