Do this walk-through on an ordinary visit, not after something has gone wrong. It takes about forty minutes and you do not need to announce that you are doing it.
Start at the front door
Is there something to hold while unlocking it while holding groceries? A handrail on any step with a rise over six inches? Is the threshold high enough to catch a toe or a walker wheel?
The path they walk at night
Walk from the side of the bed they get out of to the toilet, in the dark, at their pace. Count the obstacles. This one path accounts for more falls than the rest of the house combined.
The bathroom
Nothing to hold entering the tub. A towel bar being used as a grab bar, which is the single most common dangerous substitution in American homes. A toilet under 17 inches. A bath mat with curled corners.
Rugs
Every throw rug is a fall waiting for a bad day. Either tape them down or take them up, and expect an argument about the one from the trip to Turkey.
Lighting
Age changes how much light the eye needs. A room that looks fine to you at 45 may be genuinely dim at 78. Check the hallway, the top and bottom of any stairs, and the closet.
The kitchen
Anything used daily should sit between hip and shoulder height. If a step stool is involved in making coffee, that is the finding.
Stairs
Handrail on both sides, running the full length including the last step. Contrast tape on the edge of the top and bottom stair.
The chair they actually sit in
Can they get out of it without pushing off the arms three times? A chair that is too low or too soft is a mobility problem disguised as furniture.
Cords and floors
Extension cords across walking paths, transitions between tile and carpet, and any floor that gets waxed.
The phone
If they fall, can they reach a phone from the floor? A cordless handset in each room costs less than one ambulance ride.
Medications
Look at how they are stored, not just what they are. A drawer full of loose bottles is a dosing error waiting to happen.
Outside
The mailbox path, the trash cans, and whatever route they take in the rain.
What to fix first
Bathroom, then the night path, then lighting, then rugs. In that order, every time. The rest can wait for the next visit.