My mother was diagnosed celiac at 60 years of age, what effects/damage could be done to her health seems as she was only diagnosed at this age?

Celiac disease: Celiac disease can cause different diseases. Malabsorption can predispose to iron deficiency anemia and osteoporosis( bone loss) chronic inflammation of intestine can predispose to small intestinal lymphoma or carcinoma( cancer) celiac can also predispose to other cancers like esophagus. Liver test can also become abnormal and one can have pancreatic insufficiency.

Depends on duration: She may have had the disease a while before diagnosis. How long would tell you if she was at more risk than most for things like osteoporosis. There is growing evidence that longer-standing disease might weaken parts of the immune system. Some advocate special vaccination for Celiaca because of this. Talk to her doctor for more details.

Relax: Some people are born with the genetics/tissue type that is more likely to acquire celiac disease, but you are not born with it like blue eyes. It is likely some event or series of events eventually triggered this in your mom in the same way some get rheumatoid arthritis.There are a few associated issues her doc is likely aware of. She & her doc can sort them out if they come up.