When Reuven and Danny go into Danny's bedroom on Shabbat (Sabbath) afternoon, Danny turns on a light. No Hasid would ever think to turn on a light on Shabbat.
While Danny and Reuvan discuss the Ba'al Shem Tov, he is referred to as "Master of the Good Word." "Shem" is Hebrew for name. The Ba'al Shem Tov's name is "Master of the Good Name" - not Master of the Good Word.
The film starts with a montage of old time radio audio clips from World War II. This begins with an announcer doing a station ID for "WEAM, NBC in New York." At the time, NBC's New York station was WEAF.
The copyright date on the Universal newsreel is 1944, when events in the film are taking place after V-E Day which was on 8 May 1945.
In the scene where Danny and Reuven tangle with the three street bullies, a modern (i.e., not 1940's) commercial bus passes in the cross street in the background.
Hasidim do not use the word "God"; they say "Hashem".