There are dramatic changes in weather in this movie, which takes place during the holiday season. In the opening scene, there is snow, but then when Nikki is at the railroad yard in a scene shortly afterward, the snow is all gone and she's not even wearing a coat. In a scene which presumably is later that evening at a mansion on Long Island, there are several inches of snow on the ground again.
Nikki's hair goes through some drastic changes in an incredibly short time span without any help. For instance, from when she sings "Silent Night" to her father, to changing to go to the Circus Club, to when she sings there.
William Frawley's character (the police sergeant) gave a wildly incorrect definition for the word "MALFEASANCE". He says it means "making up a murder and taking it to the police". It actually is defined as, "The performance by a public official of an act that is legally unjustified, harmful, or contrary to the law." It's used especially to describe a violation of the public trust by a government official.
While Nikki is walking on the railroad tracks in her initial attempt to return to the scene of the crime, she is nearly hit by a speeding GG-1 locomotive. GG-1s were Pennsylvania Railroad locomotives; Nikki arrived in New York on the New York Central Railroad, which did not have GG-1 locomotives.
When Mr. Haskell leaves Grand Central Station with Nikki Collins, they call for a taxi. When a taxi pulls up, however, Nikki's luggage is already piled in the front seat though she did not walk out with any bags nor did a porter load any luggage into the taxi. The taxi wasn't there waiting for them; it was just a random taxi that happened to pull up. The sequence, therefore, doesn't make any sense, and it interrupts the flow of the story.