When Ellery goes to Kitty's apartment, he knocks on the door and says" Jenny, it's Ellery".
Guy Lombardo here is shown to be as he was in 1974, since that was when the episode was produced. Although in 1946, he would have looked 28 years younger. And the character he plays is referred to repeatedly as 'Guy Lombardo'.
The girl photographer is using blue flashbulbs which weren't manufactured until the 1950s.
The camera that the girl photographer is using at the New Year's Eve party is a Speed Graphic which were manufactured starting in 1947. Since it is December 31, 1946, this camera would not yet be available.
Ellery says you have to dial 6 numbers to make a phone call in New York City. Not true: since 1931 you have had to dial 7 numbers. This throws his would-be clue out the window. It may be that the mistake is on purpose since a 7 digit number could have been a real number.