I remember on the Cycle Oregon 2009 (Jefferson State) ride, we got into a mess of goatheads like you wouldn't believe. At one point along the ride (day 4, if memory serves), I passed over 60 people with flats. I was thrilled that before doing the ride, I remembered the problems I had with goatheads living in Ashland. I invested in new kevlar tires, thorn resistant tubes, and slime.
My bike was easily the heaviest standard bike on the ride, but I didn't get one flat on the whole trip (and I was one of the heaviest riders).
Fortunatly for me, the flaws in the belted tires didn't cause problems until after the ride.
I'm now riding on Specialized Crossroads tires