Yes the auto correction is on,but it does not correct all the time.I can make a silly spelling mistake and it will not correct it.This is my first I Phone,my last phone was a Nokia and their was predictive text,which was very fast.
I have found a app in the app store it's pretty cool haven't used it much but does work. I thinks it's 2.99 can't remember it's called Spell Check. Just search for it and should find it right away . But you have to type in the program and paste it into a email or text. I saw one in Cydia for the same price and it looked like it worked in the factory apps which is better so not sure if this helps ...