I don't think you are approaching the question from the right angle. If by 'interesting' , you mean problems whose solutions would provide a lot of value (whether you want to convert that value into money for yourself, or just looking for the satisfaction of doing some good in the world), then most of those problems are just not problems yet. Nobody has actually identified them as such.If you think of it, before google map,facebook,Uber,wikipedia etc... nobody actually knew that we needed those. The problems were there, just that nobody though of them as problems or nobody could anticipate the magnitude of the value that solving those problem would provide.
I think the guys from Y combinator (or is it from the book zero to one) say it perfectly : 'Which company nobody is building...'.Nobody is building them not because of the lack of resources, but because nobody have found a way to identify them. So to answer your first question, nobody knows how to reliably and repeatedly identify interresting problems.
As you i have been think about this question quite a bit lattly, here my though so far :
1 - The difficulty of identifying worthwhile problems can be though as a form of uncertainty, so learn about strategies to deal with uncertain environment. Zero to one, lean start-up and anti-fragility all treat this subject from different angles : in a nutshell, forget about find the right problem, start multiple small projects, iterate fast, be flexible, invest small and kill then unsuccessful project quietly.
2 - The other strategy is to leverage your particular expertise to identify problem in your domain. Depending on your domain, you might stumble into a niche problem which can generate a a lot of value for yourself (since you would have less competition)
Hope it helps