I was previously using an open graph plugin that had an algorithm for picking the image to send to Facebook in open graph. It looked first to see if there was a featured image for the post/page, then if not to see if there were any images in the post/page itself, and if not it then it fell back to a default image specified in the settings.
The Facebook plugin is (at least for me) not consistent in this regards. For posts, I'm not sure if it's picking the first image or the featured image (for me they are usually the same, but it is at least passing an image. For pages however, there's no image value being passed. I see this both from looking at the resulting code as well as the debugger. Here's a page from my site as an example, when I run it through the debugger it points out the image is missing. Is there a setting somewhere that controls this or does the plug-in not look for images on pages?
If not, could a future iteration be updated to A) Include images on pages and B) allow us to set a default image for those instances when a page or post lacks any images?
Note, I've hard-coded the like button into my template, but even when I disable and turn on the Facebook plug-in like button, I still see the same behavior. It's the halfway problem I can't get around easily. I could tell WordPress what og:image to pass but on posts it would be duplicated.