hi to all today facebook roll another update in app store but my problem remains like yours ! i test 3 devices on same cellular network and after on same wifi spot.
I use 2 iphone 5s and one ipad 3. All 3 devices have same ios 7.0.1
all 3 devices have latest fb app installed, all 3 devices was jbked with same tool
anyway in all combination on one iphone 5s FB video can not be played !
on that device i even play with fb iternal settings but with no luck, i try even on that devices various thing in safe mode !
why in safe mode, because to be shure that no tweak have connection with that bug
i try install vpn and connect true vpn but ip adress have nothing to do with bug.
if i login tru safari on fb, videos playing with no problem at all, but u want to be able to watch it on app. if somebody have some thing to try ... i will test it
that is real mistery
btw. i forget to write that i do network reset but with no luck