I've seen industry outsiders solve a nonexistent problem, or fail to solve an existing problem without realizing it, or solve a non-generalized version of a problem that only applies to one company, or solve a problem excel solves better, or solve a problem which was just a bad (now permanent) process. The list goes on.
However it happens, you greatly increase your chances of providing a valuable piece of software if you have exposure to not just a single business in an industry, but dozens of them.
Working tech support will tell you what real users are having trouble with and sometime they have really great ideas for features.
Alternately, instead of starting a new career, you could ask friends and family for an introduction where they work and just go with your original idea of shadowing people. Most SMB owners I know would be happy to let a software developer analyze their process and brainstorm about useful software. Just give them a perpetual free license for helping you develop it. They might even be interested in helping you bootstrap it. Business owners are often looking for a good investment.
I'd guess that every industry has its own specialized news sites (something like TechCrunch.com, but for bankers or civil engineers). You could try finding some of these on the web and reading them. You can also learn a lot about different industries by reading a good business paper, like the WSJ or the business section of the NY Times. There are also locally oriented news sources, like Crain’s New York Business.
I've not been consulting for big business for a while, but often if you went into a large organization they'll have a copy of trade magazines related to their field(s) in their reception.
A quick google shows there's still lots of trade magazines in print, so I assume it hasn't all migrated online because of their specialization.
other thing was to create website for open source business processes. For example you wanted to start a laundry business, you could just come to website and view best ways to do things. Like check lists and flow charts for all matters: accountability, customer service, repairs, monthly check ups.... this would put individual owned businesses on par with international chain businesses. they are constantly iterating and testing to improve. individually owned businesses are too busy to work on business sometimes. in doing this businesses would expose inefficiencies through their documented process and reveal opportunities for ideas.