I just watched the pilot and I thought that it seemed strange that when Mrs. Muir hears and sees the ghost for the first time that she did not seem bewildered/frightened/taken aback/nervous and so on. It was same with the little boy, he acted as if it was perfectly normal or fine to see or hear a strange man in their home?

Maybe I missed something or it was edited, but the director and the producer should have had her react more. She acted as if it was a common day to day occurrence to come in contact with a ghost.

It is a family sitcom and they did not have to be scared out of their wits, but they sure acted as if it was nothing out of the ordinary.

Does anyone have any thoughts about this?

If I remember correctly, Mrs. Muir was the same in the 1947 movie. It's part of who her character is, and part of why the captain accepts her, because she's not afraid of him, or to stand up to him.

At that age, it's not surprising at all the boy wouldn't be frightened by the captain. It wouldn't be any different than if it was an imaginary friend.