Most of the time, when I share my posts to Facebook and Google+, the photo and video thumbnails do not appear. Occasionally, the thumbnails do show up in my Facebook or Google+ post share, but I don’t know why it works sometimes and not most of the time.
We have no control over which images Facebook displays. Please see here:
Only the first five images uploaded to a post (direct inclusion/gallery/slideshow) will be sent to Facebook. The images size has to be at least 200 x 200 pixels.
To select which image will be used for things like Facebook Publicize, you can use a theme that supports featured images. If a featured image isn’t set or your theme doesn’t use featured images, then the code tries to pick the first image in the post or page. If no image is found, then the blavatar is used.