Not really a bad thing a shared well, as long as all the users agree to make repairs needed and can afford to do so you should be good.
I would suggest a system for the house water to clean up the hard water coming in to the home (hard on clothes, dishes, glass, back sinks and of course any appliance that uses water.
A flow test should be performed in the event you are thinking of purchasing a home with a shared well. Just make sure the neighbors are informed of the test as you will be shutting their water off for about 45 min.
Have the Realtor check the well drillers log on line through the AZ Department of Water Resource if the well was a recent drill. That will show the volume of water per min and the quality.
I live out in the Rio Verde Foothills and have a lot of experience with wells, well drillers and pump services.
All The Best!
Stew Keene / Realtor
Signature Realty Group - Inspire Realty Group
Scottsdale and Phoenix, AZ