How do you prioritize which 'frustrations' to work on?

Processing existing customer feedback has always been a problem even at large, established places I've worked for - chasing the new customer and adding features is always sexier than a general feeling of unease that requires a lot of prying to get to the root of.

Often in my experience most customers don't seem to know what the exact problem is, or can't put it into words, so having strategies to tease that out would also be appreciated.