One thing I've noticed that has generated a ton of ideas, particularly within the hospital setting I'm in, is to listen to all the questions staff members ask one another. Who's doing that? When's this happening? How do I do that? etc. They're all seemingly mundane questions that get asked on a daily basis, but they give you great insight to the daily frustrations that people have come to accept (that's why they're boring everyday questions). They also often shed light on a lot of the accessory tasks people endure in order to accomplish their main job.
As an example: in a hospital, we have the "sign out sheet" which is a list of the current patients and all of their important data. These sheets are usually manually updated and it's a very, very tedious task; you've got to make sure all the dosages are current, and they're already in the system! Anyway, I kept noticing the residents would ask one another if they had updated the sheet and realized this was a pain-point that's become an accepted part of the day-to-day medical routine. That's just one example.
Good problems don't have to elicit noticeable frustration. In fact, I'd say many of the best problems around are ones that have pushed people past frustration and into acceptance.