One side of my 91-year-old mom's face is dark. Should I be concerned or is this old age?

Did she have a fall?
If so, you will need to bring her in to the emergency room get a CT scan to make sure everything is okay.
CT scans can show if there is swelling or bleeding in the brain or a fracture in the skull.
Whatever it is from, you will want to have a medical professional look at it.

How do you mean, dark?

By "one side of her face" do you mean literally half of her face, forehead to chin, nose to ear? - or is it more localised, like a bruise?

Just to check, and not being silly - she isn't sleeping on a brand new (i.e. not yet laundered) pillowcase or anything like that is she?

If you're sure it's the skin itself that is discoloured and there isn't any obvious cause, you'd better report this to her doctor and get advice.

How long has she looked like this? Did it come on suddenly and does she have any other symptoms?

I have no idea what this symptom might mean and I’m thinking you may want to call her doctor or her insurance’s 24-hour nurse advice line.