Cassa, you're absolutely correct. There most definitely is a "cat and mouse" pursuit upon one's initial viewing of the episode. Leigh plays the part so incredibly perfect that you do "see" Grace as a plotting murderess all along during the first viewing of the episode. Then, once you realize that she has the disease and watch the episode again, you "see" Grace in a totally different aspect - even though it's still the exact same performance. Again, this is because Janet Leigh was such a fantastic actress.

She was wonderful, wasn't she? I agree Headache that she played this role with absolute perfection. If you just watch her face during the whole episode, the little nuances you see reveal so much about her character.
I love in the beginning when she is whirling around Henry's bedroom. She is absolutely giddy with delight. She floats around the room with such an air of sheer bliss.