Well, I think there may be some problem with the app try uninstalling the app from your device and again try downloading and installing the app over to your device and see if its starts working again or not ?? If you still find some error let me know what is appearing over the screen after you open the facebook application over to your device, I am also using facebook app over my tab3 and haven't encountered or heard problem like that because I can confirm that Facebook app is working fine over tab3.
Welcome to Android Central! You have the latest version installed, right? Try going to the App Manager, select Facebook, and Force Stop, then Clear Cache/Clear Data. Now try again.