If you read the comments on our Facebook 3.2 and Facebook 3.2.1 posts, you might see that the latest version(s) of the uber-popular social networking app is having a little trouble on Jailbroken iPhones. Looks like Facebook is aware of the problems and working on a fix:
If you have a jailbroken device, you may have experienced problems with our latest updates. We've identified the issue and have an update with a fix coming soon. Thank you for your patience.
BiteSMS for Jailbreak is often mentioned as a source of conflict. Until the fix is pushed out, you can uninstall it to get Facebook working, or just use touch.facebook.com to get your social on.
[Facebook, thanks Robert!]