Early in the episode is a reference to John F Kennedy Airport. This part is set in 1963, as they are returning for the new year of 1964. Until January 1964, John F Kennedy airport was known as Idlewild.
At the end while they are watching the New Year's Eve ball drop and the fireworks at the balcony, the weather was pleasant but in fact a big snowstorm was hitting NYC. The New Year's Eve 1963 snowstorm was a significant winter storm occurring from December 31, 1963 to January 1, 1964.
When the plane is coming into London Airport, the pilot says they are arriving at Heathrow. London Airport didn't become Heathrow until the 1970s.
Characters are shown drinking from lovely wine glasses with a diamond motif. This extremely well known pattern, "Diamond Point", made by Indiana Glass wasn't introduced until 1965.