I haven't had the above problems, however I do find I have a notification for a new private message within the app (i.e. the icon has a '1' badge next to it) and it really struggles to load the actual message when I click on it (i.e. it doesn't refresh the list of messages)
Not an issue on my side as its common on wifi or 3G; I suspect its more of a FB issue, it is the one app I find takes unusually long to update (and on a ip4, the performance is a bit rough at times when there are a lot of photos)