Hello all I am new but I saw this post and thought I could help out so I registered. I just picked up an iPhone 4 I am an android fan but so far I am really impressed with this device apple just does hardware right!
Ok to the question at hand I had the same exact problem and this tip fixed it 100%
Uninstall the Facebook app from your phone.
Reboot your phone
Log into Facebook from your computer not a phone.
Change your Facebook login password
Make sure new password works and log out of Facebook.
Download and install Facebook app back on your iPhone.
Login with username and new password.
That has completely fixed my Facebook app problem I hope it does the same for you as well no more force closes and it has been running fast and smooth for a week now. Hope this helps post back your results when you get a chance.