Direct Errors:
"If there is a 4th satellite overhead you will get your elevation as well - although with little else to intersect it, height accuracy won't be as good". Alltitude is not computed seperately, its does not just appear when the 4th satellite appears. Altitude is just as accurate as position but its measured in a strange coordinate system based on the center of the earth. The biggest error in "effective altitude" is not knowing where the ground is (due to landmass, shape of earth etc) and not an inherent problem with how the position is calculated.
"The first satellite draws an accurate circle; all it knows is you are somewhere on the line of that circle. The second satellite draws its own circle which intersects the first at 2 points. When the third draws its circle it will intersect only one of those points" Rubbish... its using spheres not circles and it never geometrically picks a point, at the final stage of geometry calculations there are still two points and one of them is selected via logic. If as you beleive and the article states, 4 satellites are requried for altitude, this explanation has no room for a 4th satellite.
"...and the time is spot on to the nano second time the satellite ceasium clocks are using". Wrong. Using standard C/A L1 signals, your receiver is only accurate to 1us, the bit period of the sync signal. Its actually slightly under 1us due to having 1024bits in 1ms.
"If you remember that the 1.5GHz frequency equals a wavelength of 200mm, that, incredibly, is the order of accuracy you are dealing with". Complete rubbish, that signal is never used in computing position, it is demodulated to give the data payload and is no more impressive than a radio receiver. That statement to me is a complete missunderstanding of what the singals are used for, there is never a 200mm accurate position. The sync signal gives time within 1us which gives the sphere raduis to within 300m. The accuracy does not come from the absolute size of the spheres, the final position is the intersection of these spheres.
In addition to the above there is alots of handwaving. From my point of view, these errors are so fundamentally wrong I can only beleive all the people involved with editing it don't get it.
Edit: "A satellite direclty overhead yeilds a small circle, one close to the horizon draws a circle nearly the dimension of the earth". I don't know what that means, it sounds like somebody is projecting the spheres so it can be drawn on a piece of paper. In the modelling the earth is not used, in fact its not even there. The only places the earth is used is in converting ECC back into log/lat/altitude and a sphere on the center of the earth can be used in lieu of a 4th satellite.
Rob