Apparently due to recent changes, WordPress blogs with All in One SEO will not automatically post to FaceBook. After some web searching and multiple test messages, the root cause seems to be the All in One SEO plugin not writing “og” tags right for FaceBook, so FaceBook refuses to post. Posting to FaceBook by clicking the Share button under the post works normally.
I am not sure how to fix this in All in One SEO, although my understanding is that this is a configuration error on my part. However, for now, disabling the All in One SEO plugin fixes the problem and scheduled posts are not automatically shared on FaceBook. The problem affected only sharing on FaceBook: sharing to twitter, G+, and LinkedIn continued to work fine.