Doorknobs - If the person tends to wander, you might want doorknobs that are difficult for them to figure out how to open. Change each one that leads outside and don't keep keys in a visible place.
Car - In case they happen to find the keys lying around and get outside, you might check into a safety device for starting the car. A car alarm would alert you before they were able to get in and drive off as well.
Workroom - Did the person enjoy working with saws, drills, or other dangerous power tools? Putting these in a locked cabinet is a sure way to keep them from using something that once was second nature for them. It's too easy for the dementia patient to forget the safety features of these items and harm themselves.
Kitchen - Remove the knobs on the stove. It isn't uncommon for a dementia patient to begin cooking something and walk away only to forget about it seconds later. This is a small way to ensure there aren't any fires. Take the sharp knives from where they always were and put them somewhere safe. Someone with dementia remembers from the past, so if the item always was in the drawer, don't leave it there now. Put child safety locks on the cabinet doors where you keep hazardous cleaners.
Stairway - A safety gate such as you'd use for a child helps if the dementia patient gets up in the night. Place one at the top of steps to prevent falls. Another good place is between rooms so they don't wander throughout the house.
Bathroom - Sitting down in a bathtub can be almost impossible. If your home doesn't have a shower, be sure to get a shower seat. This makes it safer and easier for the person to bathe. You also should set the temperature down on your hot water heater. This way they can't burn themselves if they fidget with the faucet.