Of course, the kickstarter/public relations aspect is not essential to all this, but Planetary Resources gets a ton of public interest and they want to capitalize on/engage with people who are interested in their mission to mine asteroids.
Building a small satellite is quite affordable, but commercial launch costs are a problem. There are several funded kickstarter projects whose goal is to deploy one or more satellites in orbit for much cheaper than what PR is trying to raise.
People also overestimate the difficulty of finding asteroids. Asteroids are still being discovered by amateur astronomers on Earth. It's estimated that there are millions of undiscovered objects. A big space telescope is an advantage but not a requirement.
other kickstarter projects:
http://www.kickstarter.com/projects/880837561/skycube-the-first-satellite-launched-by-you
http://www.kickstarter.com/projects/575960623/ardusat-your-arduino-experiment-in-space
http://www.kickstarter.com/projects/zacinaction/kicksat-your-personal-spacecraft-in-space-No atmosphere. Seeing would still be a considerable factor; getting 1 arcsecond resolution on Earth is not easy.
-No clouds
-Ability to focus on the same object for an extended exposure
-Infrared
-Can look north and south
There are a lot of advantages to this, even with their aperture size.
30 * 1000 + 3 * 30 * 500 + 3 * 30 * 500 + 10 * 30 * 100 + 25 * 30 * 50 + 25 * 30 * 50 = 225000 minutes = 156.25 days
This is not really a lot. The remaining time will be used by Planetary Resources. There is no way for public to continue using the telescope after that.
a) The vast majority of satellites are "prototypes." They're built a few at a time, extensively tested, then launched. In the case of satellite frameworks like Cubesat, they're open source and tested every time someone launches one.
b) This is not untested tech, at all. Cubesats have been using consumer technology in satellites extensively, both by startups, hobbyists, and academia (doing advanced stuff like orbital reconfiguration, atmospheric sampling, telecommunications, etc). Combined with NASA's existing suppliers for aerospace grade components, these satellites which have a really high success rate.
Colloid thrusters (or other ionic propulsion), or even a chemical hybergolic propellant (hydrazine + oxygen for example) would work perfectly for propulsion. This is a solved problem, so much so that there are off the shelf modules for cubesat propulsion.