My understanding is that GPS errors are (mainly) systematic:
This is why there are augmentation systems (Differential GPS, WAAS) built around the concept of a ground station at a known location providing offset information as to the system error, allowing further calibration of receivers in the area.
This also would explain the ForkTailedDrKiller's observations - the *accuracy* may well be 35m, if comparing the reported position to the actual position. However, the *repeatability* is rather better if all you want to do is hit the same place / waypoint again, rather than finding a spot from a given lat/long.
This would also suggest that the velocity measurement (rate of change of position) is somewhat more accurate than the absolute position.
Interestingly enough, I also used to drive a saab (9-5 with an electronic speedo), and found a pretty consistent 4mph underread accross the range - suggesting that the spedo is pretty accurate, and has a built in factor.
Other cars including older saabs with mechanical speedos tend to show a percentage error.