When Kay leafs through Bernstein' photo album, there is picture of a New York City taxi with a rectangular roof light which displays not only the word "Taxi" but also whether the taxi is off duty and its medallion number. Those signs did not come into service until the 1960s. In the 1940s, when the movie is set, New York City taxis used a variety of curved roof lights used in most other cities.
Burnsey's 35mm camera is either an Exakta V or VX. Those models were introduced in 1950 and 1951, respectively, and would not have been available during the 1940's.