I'm working my full-time job and in my startup (along with a couple of personal projects) - and I was close to burn-out several times during the past couple of months.
I always have a flexible work schedule, but I usually start around 8-10 am and stop at around 8-10 pm :).
LOTS OF EXERCISE (jogging in the nearby woods)
And I'm definitely working on getting closer to 8-10 hrs per day ...
Experience, open-mindedness, open eyes, serendipity.
Using Twitter, Google Alerts & co. is just another way of having your eyes open (really wide, in this case), but they are hardly enough.
Do your thing, follow your bliss, and problems will find you - specifically searching for one is like searching for a girlfriend at a party.
I think that not working in an industry often gives you a unique perspective that might as well make you more likely to spot a particular gap its regulars are taking for granted.
Of course you will need some insider knowledge, but oftentimes not all that much - a lot of industries develop similar approaches to solving similar or analogous problems, but with varying access to the underlying knowledge/skill needed to making it effective.
You will need to be a bit of an anthropologist and a good communicator to get the relevant information from people whose working days you plan to optimize/improve with software.
I'd say observation with an unspoiled eye can work wonders :).