In a previous post (Finding all Visio Questions on StackOverflow using the DataExplorer) I showed how to query StackOverflow to get a list of all the questions that had a tag “visio”. I asserted in that post, it was good datasource to understand your customers/users better. Now I'll show it.
I analyzed all 358 questions and here are my results.

We should revisit the StackOverflow FAQ before we go further:
The two big buckets need a little explaining: “Programming Question” category counts those questions that clearly about programming problem or code while “Visio Feature” identifies those questions that involve using an Visio feature – one that may involve using Visio as a tool in software development.
Some other categories

As I suspected there's a healthy number of questions about UML diagrams. This isn't surprising given the role of UML in software development.
The bars marked in green are conceptually related. Many people are asking about the two-way transition between a diagram and some other source. For example: getting a diagram based of a database's schema or building a database schema using a diagram as input. In some cases, people want to using Visio diagrams as a source of data and need to extract it. At other times, they need to build a diagram from simple data (a CSV file for example). Many of these questions are clear duplicates.

(NOTE: YES, I really should do another pass to weed about more of the blanks.)
What surprised me here is that I didn't see that many questions about expressions in ShapeSheet or creating custom stencils an masters.
Unsurprisingly people are interested in Programmatic Diagram Generation – it's not obvious from the chart but if you look at the raw data you'll notice people seem interested in creating Visio diagrams without having Visio installed and creating those Visio diagrams on the server-side (for example from a Web Page).
My biggest surprise was the small number of off-topic questions (per the StackOverflow FAQ). In my recollection, I flag one or two Visio-related questions every week on StackOverflow questions as off-topic belonging to the SuperUser site. These questions are more about using Visio than having anything related with programming or dev tools. I suspect the missing questions could be because those questions once migrated to SuperUser no longer have any record in StackOverflow.
Don't take my word for it. You can analyze the data yourself. The raw data is available as an XLSX file on my SkyDrive (http://sdrv.ms/K1B850)