I do not really use Facebook app, so i can't say much about it. Anyway, i think that it should be feasible, but now, where are you copying from? from a note app? from safari? or from Facebook to Facebook?
The Facebook application for iPhone is really fickle, in my opinion. Double tapping the screen in the general area that you want to copy will... most of the time... bring up the "copy dots."
Ever since Facebook updated, I too have lost the ability to copy and paste someone's status to my own status. I don't think it is an iPhone issue as copy and paste still works on email etc it is just the latest Facebook update- I hope they fix this bug in the next Facebook software update.