Investigator Hennessey (as his name is spelled in the credits) is shown sitting at his desk on which there is a nameplate which reads Francis K. Hennessy.
When Howard and Florence kiss in the park, the bi-level George Washington Bridge can be seen in the background. In c. 1953 when this movie takes place, the bridge had only one level.
The story takes place in 1953, but there isn't a male cast member in the film with a 1950s haircut. 1970s sideburns are on most, and heavy mustaches are seen on several.
An establishing shot up the Bowery to the Peter Cooper statue (before the script exchange) doesn't include the El tracks, which would have still been present until the Third Avenue El made its last run in May 1955.
The second taxi cab shown prominently is a mid-1970s Checker A12, evidenced by the side reflectors and the large bumpers. The correct Checker for 1953 would be the model A6, which resembled late 1940s GM products.
Some of the extras in the film are not only sporting more 1976 style hairstyles/facial hair but some extras can be seen wearing New York Mets caps. The Mets didn't come into existence until 1962 almost a decade after the setting of the film takes place.