Doppler
Two points that seem to me missing in the above responses:
1. Consumer GPS generally gives Doppler a considerable weight in the displayed speed--so it is not just a matter of position error deltas for speed error. Generally Doppler does better, which is why they use it. It also responds quite quickly, though not instantaneously, depending on what sort of smoothing the manufacturer puts in for post-processing.
2. Confidence from displayed zero velocity is a bit misplaced. Consumer units generally clamp the displayed velocity to zero when the initially computed value is below some threshold. I noticed they lowered the threshold on the ones I use when SA got turned off. I think I recall it used to be about 1 mph. A few minutes walking about extremely slowly with my Garmin GPS V just now with WAAS turned on and eleven well-positioned satellites in view never once displayed 0.1 km/h, though 0.3 and 0.0 appeared many times, and 0.2 often. I surmise the clipping limit in the current firmware in that condition was probably a little over 0.2 km/h.
Despite those two points, I agree with those who suggest that a _consistent_ difference between an automobile speedometer and even a very cheap consumer GPS is almost certain to find the GPS in the right of things.
Disclaimer: I'm not a pilot, but am an electrical engineer, and have used GPS a lot since 1991.