In the opening titles, Bette Davis is returning from errands, feeding birds in the park, buying flowers from a street vendor. She carries a square box tied with string that is upturned while buying flowers. Upon returning home to the Vane household, the box is opened to reveal a decorated cake for Joey and amazingly the cake looks perfect despite it's perilous journey home.
In the scene where they put the doll into the bathtub to scare the nanny: When they first pick up the doll, it has blonde hair, then when they put it into the bathtub, it has black hair, then when the nanny finds it, it has blonde hair again. This is a technique that is repeated throughout the second half of the film, whenever the bathtub death is revisited by the characters.
The family would not have continued to employ the same nanny after the daughter drowned in the bath.