Like everyone else, seniors can contract sexually transmitted diseases, and someone who's been in a stable, monogamous relationship might need an update on what's "going around." You also want to make sure that your dad isn't being taken advantage of financially.
Even if you don't double-date, you should meet anyone he's seeing regularly.
Keeping a distance may also be useful if you need to intervene at some future date.
Because your dad can't drive, you can help him plan for alternative transportation.
If she doesn't want to get to know his family, that's a good indication that she might have ulterior motives.