I'm a junior professor in math at a large state school. I was just talking with a colleague about how much thankless schlep work our junior administrators (i.e. the assistant chair) have to do.
Here is one example. We run ~75 classes a term, and we have to schedule who is going to teach what, where, and when. This is subject to all kinds of constaints: space limitations; remedial classes get assigned to grad students; Professor So-and-So hates mornings; Professor Whosit hates the evenings; and so on endlessly.
Currently our assistant chair handles this by having everyone fill out a form, and with an Excel spreadsheet. It is a huge chore, a complete pain in the ass, and totally thankless (that person assigned to teach College Algebra at 8:00 will still remember it five years later...)
It occurs to me that this is a problem that might be solved with good software. And that this is only representative of the kind of problems academics face. Get the attention of the assistant chair in any academic department (other than perhaps at rich private schools) and he or she will tell you about all sorts of obnoxious work which he/she doesn't see any way around gutting out the tedious way.
It seems that there's a potential market for software, and a potential for a startup here. (Unless someone is already in this space -- but I've never heard of anyone using such software.)
Your market would be individual academic departments (not entire universities), and you could probably sell good software for a couple hundred bucks a year. You would need to keep in mind that departments don't trust university administrators to do these kinds of things for them, which is why you see professors doing it.
Just an idea that occurred to me.