A previous update of Facebook's iOS app completely messed up a handful of features, particularly its push notification services. I'd be browsing through status updates, exit out of the app, and see a notification badge had popped up. Curious to see what was new, I'd go back into the app and check out the notifications ... only to find notifications for stuff I'd already read. This wasn't a "once in a while" kind of bug, either; it happened nearly every time I used the app.
Facebook's app has been updated to 3.2.3, and it claims to fix not only the push notifications issues but also crashes associated with viewing messages and errors involving Facebook's Places feature. So far, things seem to be running smoother for me. However, based on the feedback that this update's received so far on the App Store, it hasn't been a universal fix. Download the update and see for yourself if it fixes any issues you may have been having, then let us know in the comments if the Facebook app is running better or worse for you.