-- Last Updated: Jan-31-13 2:12 PM EST --
First of all, you are going about this calculation of error backward. When someone says the error in MPH is well within 0.1 (actually, approaching 0.001 in a lot of cases), that doesn't mean you can just use that very conservative figure of 0.1 MPH error to come up with an error in distance measurement that adds up the maximum possible error over time. That kind of logic in reasoning tells me this isn't worth my time, but what I wrote below, I wrote earlier so I'll leave it pretty much alone.
The distance measurement is determined via location determination over time, not via the calculated speed during travel, so a generous assignment of 0.1 mph error isn't your base data when making error-in-distance calculations. Any place your GPS makes a location determination, it may be off by a certain amount - no argument from me about that - but these errors are not continuously additive, because the machine does not rely on previous measurements to determine its current location as time goes by. Also, plus and minus errors relative to the direction of travel average out over distance so they really are not cumulative. Errors to the right and left, relative to your direction of travel, have a much smaller effect on the measurement of distance traveled than those in the plus/minus direction (it's just geometry), but further, since simply observing location readings on the machine suggest that the error is more of a slow drift than totally random, right-left errors due not automatically insert zig-zags into your route that are as severe as the total possible error. Your way of adding up this error suggest you expect that worse-case situation, but in actual fact, one does not see this happening when monitoring course.
So, assuming once again that determination of location might be off anywhere from 0 to 50 feet in any direction, if you use the GPS to determine straight-line distance between two points, it uses ONLY THOSE TWO POINTS to determine the total distance between them. If those two points are a mile apart and the error is 50 feet or less, the most the error can possibly be over that straight-line distance is 100 feet, and most of the potential combinations of distance-direction error will result in a total error that is much less than that (geometry again).
I really can't understand why you make these errors out to be so huge, and the things you say makes me think you've never played with one of these machines or compared the location readings to actual locations on a map (you can plot points on modern topo-map programs to within a few feet pretty easily). My GPS is the cheapest model I could get, and I've taken it on plenty of walks in my neighborhood and found the accuracy to be enormously better than you describe (I go for lots of walks in the evenings and use to take the GPS with quite a bit). If I mark waypoints along the route at the centers of intersections (for easy map reference later) and plot them on a topo map afterward, they are almost always accurate to within half the width of the street I was walking on, and almost never off by more than the full width of the street (that's about 50 feet). Also, when walking the same one- or two-mile route many times over many days, the total distance always comes out to within 100 feet or so. Try it yourself and see. Error is not additive in the way that you described, but it does add up in the way I described above, which turns out to be much less severe than your assumptions.
Finally, I really can't imagine you have actually tried to calculate any of these errors you are talking about when a recent post of yours shows that you wouldn't even think twice about interchanging knots and mph as if they were equivalent. Interchanging units is not a sign of familiarity with this topic.