No sooner did Facebook 3.1 [Free - iTunes link] finally bring push notifications to Facebook's iPhone app... then a few bugs popped up. Proving Apple's iTunes App Store can turn around updates with lightning speed when they decide to, an update has already been released to squash those bugs and get everyone updating, friending, event inviting, and otherwise getting social with it as fast and furiously as possible.
Does Facebook 3.1.1 fix things for you? Let us know in the comments. And if you're still having issues, let us know that as well!