Can you copy/paste in other apps, like in the message app? If so then it sounds more like a FB app problem; not an iPhone problem. If it continues then I would delete the FB app and reinstall it again from the App Store.
When I use the newest version of the Facebook app on my 3GS and on my old iPod Touch 4th Gen., I could never be able to copy and paste other than when I posted statuses or comments. I don't think I am able to copy and paste on the mobile site, either. The feature is just not available.