Don't seek problems -- seek solutions. Avoid all problems :)
One of the hardest things for a big company to do is move fast. Startups typically have very limited resources, so the only way to move fast is to not spend very long on any one problem, and that's generally going to mean avoiding problems that are hard. What I'm really advocating here is that you look for the easy 90% solution that seems almost the same to the user but only take you 1% as long to implement.