My mother had moderate dementia and has developed this horrible habit of picking at herself non-stop creating sores. What can be done?

This obsessive compulsive behavior is quite common with dementia patients. Even nursing homes have a heck of a time battling this and infections can occur.

I'd talk to her doctor and ask if there is an ointment that can help keep the open spots from getting worse, and also ask advice about how to bandage the area. Caregivers have tried gloves for the elder, to very limited success. This seems to be something to control rather than eliminate, but maybe your doctor has a solution.
Carol