The position of Melanie's handbag when she visits her father.
The Ariel character has a neatly trimmed and partially shaved beard, while explaining payes (side curls). Ultra-Orthodox Jews do not shave any part of their beard or neck.
The shot of the newsstand shows the Israeli newspaper "Ma'ariv". The movie takes place in the Williamsburg section of Brooklyn, home mainly to Chassidim of the Satmar dynasty who have been extremely anti-Zionist since the mid 20th century and probably not customers of "Zionist entity" publications. Also, the English-Jewish paper "The Jewish Press" is on display. Since Yiddish is the first language of most Williamsburg chassidim the main papers on display should be in the Yiddish language; Der Yid and/or Der Blatt are the preferred reads.
The Rebbe's daughter Leah says to Emily (Melanie Griffith) that her brother Ariel is brilliant, commenting, "He's what Mozart was to music." This is a mistake. A strictly observant Chasidic girl like Leah would never have heard of Mozart. Not only are girls only minimally educated, even boys learn nothing of the "Western," i.e. outside world. Even the Rebbe himself, though he MIGHT have heard of Mozart, wouldn't have known anything about him.