Is it OK to place cameras in a house to monitor my dad's care?

Yes!

In FL. When my 93 yr old Alzheimer’s dad’s fall risk increased we did put cameras in his hall and bedroom area (places where he had the greatest Risk of falling.). He had a caretaker 24/7 but we were still concerned in those areas due to the distance from the caretaker at night and during naps.
when he moved to an ALF we put the cameras there also. Living area and bedroom views. This came in handy as he fell three times and we saw him in camera long before any of the aids saw him. We saw how he fell and got him a nicer walker and an alert button. Then the camera caught a nighttime aid slapping and pushing him. We would never not have cameras now.
Interesting point: the aid who hit him was the only one to complain about the cameras.

Ktrojano: It would be deemed okay as long as you let his caregivers know ahead of the placement of the cameras.

I live in Washington state, and cared for my dad for 4 years. He passed last year at age 98. He was a fall risk, and on the warfarin-beta blocker A Fib protocol, so falling with no one knowing could have killed him if not caught quickly. For awhile, he was able to stay in his home with me prepping meals. We had a camera there. No issues.

When his health turned and he lived with us, we had a camera in his bedroom, which he knew. So very glad we did! I always watched that he got into bed ok, and he fell twice. He was 96 at the time. We were able to get to him quickly (he had the main floor bedroom, we had the upstairs), which allowed us to get official medical help quickly, too, by calling 911. So I am a fan of cams, when used appropriately.

Your home, your decision. I can't think why you should not do this. To be quite honest, this being techie San Francisco I never go ANYWHERE without assuming I am on camera, whether in a house or in front of a house. A good suspicion to have, and curbs my propensity for wanting to steal a tiny succulent off a special specimen!

While my father was still living in a home alone with his dog, we used a camera in a main room that could pan through the kitchenette/living room/sunroom. The reason it was important is that the sunroom had a dog door to the outside. We went to my father's home every night for dinner, and upon leaving would insert the slider that closed the dog door (the dog would bark outside at night if she had access). My father had moderate dementia at the time. I wanted to make sure I saw him up and about in the morning and that he had opened the dog door closure. It kept me from having to go over to his house earlier than late morning which, was better for my schedule. A caregiver that came once a week knew of the camera and didn't care (it didn't cover an area she was in much). It was enormously helpful to us.

You need to study your own state's law regarding this. For instance, some people put dashcams in their own car, and then in some instances get in trouble when they erase the video, because it can be considered evidence. I don't think it happens a lot, but it's usually an issue they never considered when they put the camera in the car in the first place. (this particular issue only relevant for cameras that record, but still, an example of unanticipated issues)

Ktrojano, regarding placing cameras around the house. You need to let the caregiver know there are cameras in place.

Sometimes this can backfire. My boss had a long time caregiver for his wife [she had Alzheimer's] and the wife and caregiver were a good match. Out of curiosity, my boss decided to install cameras for no reason other to see how his wife was doing.....

After a couple of weeks the caregiver gave notice to her Agency that she was leaving that assignment. She just felt so uncomfortable having cameras on her while she worked. I don't blame her, I wouldn't like it if my boss put cameras in my office. He had a difficult time finding a new caregiver that his wife was happy with, she kept asking for her previous caregiver.

Just food for thought.

In your home it is legal to place cameras.
You can place them in common areas.
You can not place them in areas where a person would expect privacy. (caregiver's bathroom, bedroom)
In some states you need 2 party consent to record audio so check your state's code on that if you record.