I'm guessing people waste time copying and versioning files, and emailing updates back and forth, losing old changes, etc.
Like I have gone through voter mailing data for a political candidate and filtered it, removed individuals who's addresses were outside the area or who hadn't voted in the last election, combined individuals with the same last name and the same address, then transformed it into a format suitable for address printing.
All that is pretty easy to do with code. If you wanted to go through several thousand by hand though in an unsorted list, that would be a pain. Businesses will have similar requirements... like taking sales data that is already entered and formatting it for a report.
Where non developers waste money is doing a repetitive time consuming rules based task on a computer without automating it.
Ancedotally, non developers also tend to undervalue their and their employee's time. If you are paying an employee to do a task, if it's not absolutely essential or doesn't have a ROI that's higher then money you are paying the employee per hour to handle it, it's time to consider how important that task is.
Finally, again ancedotally, non developers often won't invest in maintenance costs, and instead end up paying for time sensitive repairs or fixes, because they are easier to reason about. A coder is more likely to expect things to break, code to rot, etc. This can be in objects, services or in underpaying trained individuals so that their is a high turn over rate, where better pay might reduce that. Costco for example makes money despite it's higher pay because they have to train employees less. I think high pay also tends to reduce employee pilferage.
Members of the first group, generally a bit older and less tech savvy, see these problems as actual skilled work, which needs explanation. "Then you got to move your mouse over here and click, when this pops up you need to …"
People from the second group realize, that they are doing dumb work and either do not care or realize, that a computer should do this. If they have seen a solution in the past, they use it. For example using Doodle instead of e-mail to schedule an event or using Dropbox or Google Docs to collaborate.
They might even come up with a process, which removes the need for the manual work, for example by putting the data in the right format in the first place. What they often can not see is, that you could hire somebody to connect the systems let alone use some Unix piping magic on their own. Also they do not consider the implications of using a consumer solution in a business setting like security concerns, fragmentation etc.
I'm guessing a lot of business owners might dismiss good ideas as being too difficult/expensive when they're actually easy to program.
Many non-developers only see as far as what paper accomplishments they have already created with their projects. Programmers, on the other hand, see further possibilities in data entry, management, and reporting, also methods to reduce the amount of work that could be done.
Sometimes that also leads to that XKCD cartoon, where non-programmers think the computers can do anything, or think that an automated X is the way to go. Seasoned developers can offer valuable insight on what might or might not be a good idea and provide wisdom on why.