For instance, I recall sitting next to a table of 9/11-truthers meeting up at a coffee shop. Their discussions kept circling back to the sheer implausibility of a fire causing structural beams to buckle. People don't have intuition for jet-fuel-hot fires; nor skyscraper-high gravitational potential energy. Similarly, the dynamics of a high-speed bullet is so far outside people's intuitions that they derisively call its behavior "magic."
I'd like to hope that at least problem 2) could be ameliorated if good laboratory-based educational experiences were widespread enough; the terribleness of everyday intuitions smacks you in the face quickly when you try to do even a basic experiment. On the other hand, maybe the old dictum holds true that education benefits those most who need it least.