On the Ride with GPS help site, there is an elegant and detailed explanation of why there is often a discrepancy between the elevation you see on a route you create and what you instantly read off your GPS while you are actually following the route.
GPS is highly accurate in the horizontal plane, but very poor in the vertical. This is due to the angle between the line of site to the various GPS satellites, and the ground. Small errors result in big differences in height, but not big differences in location on the earth.
