Update: As noted by commenters below, you might want avoid this 5.1 update. It appears to have made the app unusable for some.
Update 2: Facebook gave us this statement:
Facebook found the issue and have addressed it server side. It should be working fine as of 30 minutes ago.
Facebook updated its iOS app today to version 5.1 with a number of new features including the ability to send real “Facebook Gifts” (for U.S. users)—a feature previously only available through the desktop app. There are also a few new messaging and sharing features included:
• Swipe left anywhere in the app to quickly see who’s available and send a message
• Add friends you message most to the top of your Favorites
• Share multiple photos fast
• Give real gifts to your friends using Facebook Gifts (US-only)
• When sending messages, see who’s active so you and your friends know how soon to expect a reply