A bus with a SEPTA symbol passes by, SEPTA operates primarily in Philadelphia but didn't start operations until 1965.
Sam claims he can't play the piano, but it is later established that he had a piano teacher and played Carnegie Hall himself. Later, he has recovered his swiss-cheesed memory in Piano Man - November 10, 1985 (1991) and Pool Hall Blues - September 4, 1954 (1990) he was playing piano with Violet Walters (Shari Headley).
The audience for the second concert is the same (people, clothing, and seating arrangement) as for the first.
When Sam is looking in the mirror to see what he looks like, you can clearly see (Scott's) jacket shoulder right next to the actor playing the character "Sam" just jumped into.
Both times when the strangler is attacking an intended victim, there is clearly no pressure from the strangler's cord on the victim's neck.
When Sam and Al are running through Central Park looking for Michelle, Al's feet are kicking the leaves as he runs, despite being just a hologram.
In the opening scene, both World Trade Center Towers are lit up and clearly visible in the New York skyline. However, the leap date is February 6, 1964. The design for the World Trade Center towers had only been revealed the previous month, on January 18, 1964. Groundbreaking wouldn't occur until August 5, 1966, and construction the second tower wouldn't be completed until 1972 (with the dedication on April 4, 1973).
A poster for the Broadway musical "Sweet Charity" is seen during an establishing shot. However, it did not have its premiere until January 29, 1966, almost two years after the events of this episode.
A bus features an ad on its exterior for "Studebaker Model Preview", but the car featured on the ad is a Studebaker Lark station wagon from 1962 or 1963, making the ad up to two years out of date. More, "model previews" of new cars in the 1960s would typically take place in the late spring or summer months, before being available for sale in the fall. Typically, they did not take place in February, when this episode is set (The notable exception to this rule was the Ford Mustang, released as a 1964-1/2 model in March 1964).
In a couple of the New York street scenes, 1970s and 1980s cars can be seen.
Shortly after Sam leaps in, he meets a neighbor of the "leapee", a French woman, who is soon killed by the strangler. Sam's mission is to save Michelle from the same strangler; it makes no sense that there is no concern about saving this woman from the same fate.