This problem occurred to me few days ago where i tried re-installing the Facebook app and rebooting the phone, but nothing made the images load. There was proper data connection from the service provider Vodafone and other apps and pages were loading properly. Also i observed that the images were loading perfectly fine on a Wi-Fi network/Hotspot. The app was giving problem only when using the data connection from the mobile network. This made me to conclude that the problem was not with the app itself because the same app is loading properly on Wi-Fi internet. And it cannot be the network problem also because other sites were loading.
Then i realized that the problem is with the Vodafone gateway servers which are not letting facebook servers load the images to the phone. Here the gateway or access point we selected was portalmms of Vodafone. I changed the APN to www and Voila it started working. Images and videos were loading properly.
So if you are facing the same problem as i faced, I advice to change the APN to www or the right APN for your network and try to see if they work.