This is interesting. I don't know if it's something with my phone specifically, but the whole thing just lags by a couple of seconds whenever I try to type something. It's so bad that I'm usually done typing a couple of words by the time the first characters come up on the screen ..
If you can, take it in to an Apple Store. It really sounds like you have something going wrong in hardware. Like vondur said, it sounds like bad flash memory.
