Piltdown, It is quite true that the level of GPS error is not known (because of course, if the total error was known then it could be corrected for) and maybe in the future a clever mathematician will discover a way to derive that error...
Generally speaking, that GPS error is based on the number of satellites that the device can "see". The more satellites available, the lower the error. Since the Russian GLONASS network was opened up, modern GPS devices (such as the Garmin Glo and GNS2000) can now access a wider constellation of satellites, which greatly increases the number of satellites that are visible to the device, and thus, decreases the error.
In decent environmental conditions you can expect to see your position +/- <10m which is pretty good for tracking and proving.
One other thing that is not very well understood by the GPS using public is the broad number of environmental factors that can seriously affect GPS. Obviously anything that blocks the receivers view of the sky is a problem, but I have also had guys tell me about instances where a poorly shielded radio messed up GPS when set to a particular frequency, or where GPS dropped out when flying over a particular area - which turned out to be a truckstop where a sleeping trucker may have been trying to stop his boss from tracking his nap! Its these kinds of things which could be elaborated on in a post-PPL classroom to augment understanding about the reality of these magic boxes.