Spotted twice is the use of 1967 Chevrolet taxicabs, even though the time frame for the film is late 1965 through the end of June 1966. The 1967 models would not have been introduced until the Fall of 1966.
When Rosemary is in downtown Manhattan during the Christmas season of 1965 (her baby, we are told, is due to be born in June 1966), the title of the movie on the marquee of Radio City Music Hall is The Happiest Millionaire, which didn't open until the Christmas season of 1967.
Mr. Nicklas, the building superintendent, refers to the large piece of furniture blocking the closet as a "secretary", but it is in fact a "highboy" dresser. A "secretary" is a secretary desk and is much different in design than the "highboy" dresser shown in the film.
When Rosemary visits Dr. Sapirstein in the last act, his office manager tells her that the tannis root amulet she wore gave off the same nasty smell as the doctor's aftershave, but Dr. Sapirstein wears a beard. But then, the secretary says "But then it isn't is it?" meaning she realized it couldn't be his aftershave she smelled.
When Rosemary is waiting to see Dr. Saperstein in the waiting room (right before she walks out in a rush), she is wearing red lipstick. Moments later, she walks to the phone booth and she is wearing light pink lipstick.
At Rosemary's party, Guy steps from behind the bartender to accept a drink in a closeup shot. In the following mid-range shot, from a different angle, he is shown in the background stepping up again to take a glass from the bartender.
During the dinner scene at the Castevets' apartment, Minnie hands Guy a slice of cake with her right hand while licking icing off her left index finger; in the next shot her left hand is offering Guy the cake.
When Rosemary comes home and makes her first complaint of her pregnancy pain to Guy she goes to sit on the sofa and a Scrabble game board is seen on the coffee table. When Hutch comes to visit a few scenes later, several days have passed in the plot and the Scrabble board is still in the exact same place even though Rosemary and Guy played a game of Scrabble in between these two scenes.
The ticking of Guy and Rosemary's bedroom clock is used very effectively at several points, most notably during Rosemary's "dreams." Yet when Rosemary demands to see Guy's shoulders, to see if he has been "marked" by the coven, we cut back to Rosemary, and the electric cord from the bedroom clock is plainly visible. Electric clocks don't tick.
The doctor tells Rosemary June 28th is the day of her expected delivery, NOT the date for her next appointment. She found out she was pregnant at the end of October, and the doctor wanted Rosemary to come in the next week for the blood sample, hence why blood is written on the calendar in November.
Rosemary cooks a steak for only a few seconds on each side and then begins eating it, indicating a pregnancy craving for raw meat, but when she cuts into it, it's very obvious the steak is now fully cooked.
When Rosemary is in the laundry room with Terry, we hear the washer buzz and Rosemary throws a capful of softener into it. We hear the distinct sound of the liquid hitting an empty washer, when it is supposed to be full of clothes.
The goof item below may give away important plot points.
When Rosemary and Guy are arriving back at the Bramford, and notice all the commotion about Terry's "suicide," Guy informs a police officer that she was staying with the Castevets in Apartment 7E, yet later in the scene when Guy and Rosemary talk to the Castevets, Guy says that he and Rosemary live in 7E. Even though their apartment used to be the back part of the Castevets, there would not be two 7E's in one building.