Continuity mistake: When Rosemary has decided to sneak over to the Castevet's, she removes the towels from the closet shelves. She then tries to shut the door by pushing the towels (on the floor) into the closet. We see that the closet door does NOT shut all the way. Rosemary goes to get a knife, when she gets back to the closet, the door is completely shut, and she must now turn the knob to open it.
Continuity mistake: Rosemary tries a third time to figure out the anagram with the Scrabble letters and comes up with "elf shot lame witch". She tries a fourth time and comes up with "how his hell fact me". She decides to give up and begins putting the letters away when she has an idea and pulls the book close to her and we see the wrong set of letters back on the floor "elf shot lame witch".
Trivia: The director, Roman Polanski, started the trend of an actor walking into a room and then going to the left, or right, and disappearing behind a wall and the audience when they first saw this shifted to their right, or left, so they could see around the corner. I don't think the director expected this but it did happen.