This movie was used as the primary example of filmmaking on-set in Sidney Lumet's book "Making Movies" as he was shooting it at the time of writing.
At the Sabbath meal the assembled group dances to a "niggun" (wordless melody) that is traditional among Lubavitch Chassidim. It is usually sung as a preparation to one of the Rebbe's discourses being repeated from memory, though; not as a slow circle-dance.
Sidney Lumet confessed in his biography that when he and the crew came to 47th street district of NY for the spotting before the production of the movie, they were watched very closely by the hundreds of guards men who patrol in this vicinity, among the biggest diamond exchange center on the planet, where billions of dollars in jewels are stored in ultra security stores.
The scene at the wedding, where Melanie Griffith's character is briefly seen and then vanishes, was also seen ten years earlier in "The Verdict" with Charlotte Rampling.