I think what was happening was that the Relative Image URLs WordPress plugin caused breakage that Farcebook didn’t know how to handle. I recently made HTTPS mandatory for alfter.us, but I don’t think the Relative Image URLs plugin was stripping off enough. The URL for the image below is https://alfter.us/wp/wp-content/uploads/2014/10/apple_iie_larger.jpg (used to be http://alfter.us/wp/wp-content/uploads/2014/10/apple_iie_larger.jpg). It should’ve been trimmed to /wp/wp-content/uploads/2014/10/apple_iie_larger.jpg, but it appears the plugin only trims off the protocol at the beginning (http: or https:).
I’ve disabled the plugin. There should be a photo of an Apple IIe attached to this post. If this ends up working, consider this a warning to not use the Relative Image URLs plugin if you want all of your blog posts to show up on Farcebook. (Google+, by comparison, was not affected.)