There was a recent inquest into a yacht grounding in Sydney during an overnight race where a couple of VERY experienced (like 20+ Sydney to Hobarts) racers died. One of the findings was that in some conditions, even the best GPS (when not using RTK etc) can be several hundred meters off.

On the other hand, velocity measurements by GPS use a doppler type calculation, which is completely different physics to the position calculation. Velocity and heading should be pretty accurate once you get above 1 or 2 m/s.