Try running multiple apps on your phone while you track the ride. Compare then. Run MMR, Strava, Cyclemeter, etc. And see the differences. Does Map My Ride allow you to set your wheel circumference? Do you have it set on default or did you measure yours?

How much is it off by? I'd assume some measure of error. What model phone do you have? Could be a phone issue with GPS recognition. Are there trees in the area that could stifle the signal?

You notice the speed drop while in real time mode...it's not going to be laser precise.

How much of a distance difference are we talking here?