A little shielding is enough to protect the CPU from permanent damage for a while and error correction circuits using 3-7 or more CPUs running in parallel is way cheaper, even including engineering costs, than a single CPU.
Even with the troubles, one hell of a success for $70,000.
Not really, depending on the performance you want:
http://www.intersil.com/en/products/space-and-harsh-environm...
It's a little over $100, which isn't all that much when you consider that this is a CPU that has been used successfully in space before by NASA.
(I remember a short while ago on an electronics forum there was a discussion about either this or a similar project - can't remember - where someone bet that they were certainly going to fail because they weren't using rad-hard parts. This data point certainly supports that.)
Also, any compliance issues around rad hard components (they're also used in nuclear weapons, and fairly restricted as a result)
Most compliance issues are barriers to entry but are largely overblown. In fields like aerospace and nuclear weapons the most critical requirement is abundant reliability and lifetime data which is why, regulation or no, you will never put something like an Intel 60nm or lower processor into a critical $100 million satellite.
SpaceX is standing on the shoulders of what NASA and other space agencies have been doing for decades. Government agencies spent billions of dollars developing space exploration and SpaceX is able to use that knowledge to cut costs and take the next step.
It doesn't need to cost billions of dollars to travel into space anymore.