If you haven't done so already, remove all throw rugs from the house. They're a particular tripping hazard for someone with dementia because of brain changes brought on by the disease.
First, throw rugs create visual confusion. As depth perception changes, the shift from a light carpet to a darker one, for example, can be interpreted by someone with dementia as requiring a step up or down. Second, diminishing muscle coordination can create a shuffling step, which means a smooth surface is better than anything the foot might get caught on.
Ideal: wood floors or wall-to-wall carpeting all in one color, from bedroom to hall to living room.