Near the end, in the train station, the lady in the leopard-skin style hat is behind Evie. In the next shot, the same lady is standing at the information booth as Evie arrives to answer the passenger page.
In hotel coffee shop, Evie eats a sundae that keeps refilling itself.
The magazines behind June are the same two evenings in a row, but very different during the morning in-between.
The opening has a Pennsylvania Railroad passenger train with a steam engine. Steam operation ceased in the 1950s, and by time this film was made in 1963, all trains were diesel powered.
While on the 7th floor, Harry twice presses the "up" button for the elevator, even though he intends to go down to the 3rd. When the elevator arrives, it is indeed going down.