Some things that stood out to me:
We asked better questions than mainstream media. I have no trouble believing this is the case (having been on the asking and receiving end of bad questions), and the implications are fascinating: What could be possible if powerful people were presented with interesting questions more often and therefore enjoyed talking to the press more? How can the skill of asking thoughtful, meaningful questions be learned/taught?
Part of Elon's answer to Claire's question about neuroscience and brain-computer interfaces revealed a lot about how he thinks: “We have a tertiary layer [in addition to the cortex and limbic system] in silicon, but the communication with that layer is very constrained, like trying to drain a pool with a straw.” Thinking in systems, connecting concepts, and explaining things with intuitive analogies.
Elon described his approach to assessing ideas: The idea with the best reasoning should win, not based on the prominence or stature of the person who said it. Hence, questioning authority is/can be a good thing. Also, take the approach that you're wrong by default and try to be less wrong.
The way to get the attention/time of anyone (including someone as busy as Elon) is to provide clear value. He stayed for longer than promised because he enjoyed the questions.