GPS measures average speed (delta position vs delta time). Radar guns measure instantaneous speed (doppler shift).
GPS also tends to be less accurate in a partial Faraday cage (like a metal vehicle).
Bottom line: don't expect GPS to get you out of your speeding ticket with a tech-savvy judge.
Having said that, it's not especially strong evidence since it's pretty trivial to fake. However, in this case the title is correct: it contributed to him getting off because it gave him the confidence to challenge the ticket.
On that note, my father has a BlackBerry smart phone and his Endomondo GPS tracking app states all sorts of weird things. He went for a few mile long hike and it thought he traveled a few hundred miles across the San Francisco Bay Area. (And yes across the bay.)
No, they use a single pulse and measure it's Doppler shift.
This will allow for far more precise tracking of your speed at any given moment.
Where people would like this is to do dead reckoning when a GPS position isn't available (e.g. in tunnels). However, it turns out that it is completely useless for that, for the exact reasons the GP describes.
But it doesn't seem that likely.