You just have to train your mind to see problems everywhere. As buro9 said, be inquisitive, and question everything... I can't even read this specific Hacker News comments thread without thinking of ideas...
The idea that comes to mind right now is how to solve the "I don't have an idea" problem. I start to wonder if there is an opportunity to create some sort of online market place for start-up ideas, where the the hacker news audience could collaborate with one another and refine start-up ideas in the earliest stages of thought. But then I start to think of other problems in creating this on-line collaboration tool. For example, I realize that there might be the problem that not everybody wants their ideas completely out in the open, but yet those people could still benefit from this initial collaboration and feedback. People want people to poke holes in their ideas before they invest too much time in them. It saves time. That's a problem worth solving. For example what might take a person days to figure out in terms of concluding an idea doesn't have legs, some random person on Hacker News might shut down in minutes. It could be as simple as that the idea has already been successfully implemented, or any number of other reasons, etc. And so I start to think of a solution to that sub-problem, that maybe people should be able to build reputation, and a trust rating, which would allow people to see the ideas of people who have similar trust/reputation ratings. I start to wonder if maybe the Hacker News karma could be a variable in determining an initial rating, etc, etc, etc. I wonder how much control an idea person should have in filtering who has access to read the ideas, whether they should be able to have Friends who can always see everything they do, etc. But then I start to think where could this collaboration tool go in the long run? If it was successful what would be the next step? Would the next step be about how to help hacker news members form actual partnerships to work with one another in implementing the ideas? Etc, etc, etc...
In sum, ideas are everywhere. Question everything. And read Hacker News comments! I doubt there is any more critical place on the internet in terms of a community of people pointing out the flaws in every little (or big) thing. Hacker News comments are a great place to discover ideas (problems, same thing).