Cate, one problem that can occur with any well and in particular a dug well can be bacteria. This typically is discoverd during water tests associated with a buyer home inspection.
The bacteria problem can be easily corrected with a bleach treatment but bacteria can come back another time and you do not know it unless you have your well tested again.
I recommend installing an in-line UV system that treats (purifies) the water as it passes into the house. So long as the UV light in the system is working any bacteria in the water will be killed off. Well companies can supply you with the information on these systems.
This is just one comapny that makes UV treatment equipment. I have no connection with them just found them from a web search.
http://www.freshwatersystems.com/c-1...FUSo4AodMxdBCw