Yes, my wife could only get Facebook to work on wifi or 3g. It would not work on 4g. However, after the latest software update for her phone and Facebook update she says it works.
Weird, my issues are with trying to access FB on WiFi. I can get it fine on 4G or 3G but it refuses to work on WiFi. Everything else seems to work on WiFi.
My FB works fine when I'm out and about using 4G/3G, but as soon as I get home and the phone connects to my home wifi network, I can't connect until I reboot the phone. It works fine after the reboot.
I'm assuming it's a Facebook app problem, or else they forgot to account for some difference between Gingerbread and newer OS releases. Can't wait until they fix this crap!
What's facebook? .... really I do not like using the mobile app all that much. My current phone does not even have it loaded. I use Tweetdeck with my two primary twitter accounts and facebook all tied in. I have not been having any noticeable problems via that setup.