Oxygen needs- does the patient need supplemental oxygen, were they on supplemental oxygen before being admitted to the hospital
Antibiotics- is the patient requiring IV antibiotics that need to be monitored in the hospital, or are they on oral antibiotics that can easily be taken at home.
Other medical conditions- did this infection subsequently effect other medical issues, and are those issues under good control
Functionality- hospitalizations of the elderly often cause them to get weaker, less mobile, decreased endurance, etc. Is the patient strong enough to go home and take care of themselves.
Most hospitals will have a discharge planner or a social worker that helps coordinate patient discharge, and I would encourage you to talk to this person to get additional details of how your mother is doing and what the plan is for getting her home.