The author's point is that too many start-ups are creating fun apps that give little moments of joy rather than ones that noticeably and significantly make life easier or better for people. You can criticize the author for trying to be controversial and write something he knows has a good chance of making the front page of HN; as we've all probably noticed posts with this general sentiment are definitely in vogue right now on HN, but I think it's worth moving on from that and noting what he defines as big problems.
I think all the problems he lists we can agree are 'big' in the sense that they create a lot of confusion and inefficiency in society. In the case of medical records, 'solving' that problem could literally save countless lives.
On a related note, I disagree with the author there are big problems in society that start-ups can't solve. I think there are plenty. For many I'm guessing the idea behind 'Kill Hollywood' springs to mind. For me, it's the ubiquity of advertising in society. Personally, I'd love to see Facebook, Google, and co trying to change the world to reduce the concentration of it in our lives, unfortunately it looks like they're more interested in the opposite.