Hello since I am new to website design I am not sure if this can be done or not. I think it can since alot of sites use maps. Below I will post what my client needs, I need to know if it can be done, how hard will it be, and what type of software, and coding will need to be done.

We want a Missouri map with all counties that can be color assigned to each inspector. Then the counties need to have an editable field to add notes and details for the assigned inspector, this can be a pop-up window. The county names need to appear on the main view of the map. The notes can be printed either by the inspector, by the county or a complete list of notes from all counties.

It sure is possible.
You could either generate the image on the fly through PHP ( could be hard )

or id look into the google maps API and see if that can do it.
I would assume sho, as it would just require some overlay colours and a few overlay divs...

Humm.
Could be hard, but im sure its possible.