Aha! Okay the iPhone lacks WAAS it turns out. So it can be less accurate than other GPSes, contrary to what I said above.

I remember those numbers from my old Garmin eTrex Legend (which is what I used for geocaching). Those do have WAAS support, but they also aren't very sensitive, and my experience was similar to yours, except I thought it was more fun than you seem to have.

I think the discrete increments of distance is probably due to the discrete number of satellites it had fixes on.