In my experience, finding a random problem is only a small part of the battle. What kind of customer do you want? The problems at Fortune 50 companies are very different to the problems of 20-man shops. 37Signals made their mark on the world by recognizing that, and by focusing on the latter.
They were able to do this, probably, because that was the size of their own company, and they were likely scratching their own itch. That gave them insight into what they needed, and the problems they had, which gave them a bit of experience that they never would have had otherwise.
So, what kind of customer do you want? There aren't very many good solutions for 360 feedback, but the target market for those kinds of products are enterprise customers, and they're painfully hard to sell to.
What kind of problems can you solve? If I told you that we had problems calibrating our nuclear cooling systems, is that something you can solve? Is that a problem you can even approach?
These things matter, really, and it's hard to just spit out problems at random without knowing the kind of problems you're looking for. On top of that, there's very little practicality to someone trying to solve a problem that they don't experience themselves... or, at least, it rarely works.