Incorrectly regarded as goofs: A man is wearing a cross in the opening act. He is a priest; not every man in town is Jewish.
Continuity: The sun angle changes several times during the matchmaker song sequence. Most obvious when Chava is pushed onto a sunny pile of hay that was in the shadows seconds before.
Revealing mistakes: During the dream sequence, the wires holding up Fruma Sarah while she is "flying" are visible.
Continuity: During the first few shots of crowd holding candles on their way to the wedding, the sun changes positions above the horizon.
Continuity: During the dream sequence, Tevye says that Golde's grandmother "looks good for a woman who has been dead 30 years." However, later during the song "Do You Love Me?", Tevye says the first time he saw Golde was on their wedding day 25 years ago. How does he know who she is when she died five years before he even met Golde?
Factual errors: In the movie, the fact that Tevye wants to dance with his wife, as well as Motel and Tzeitel in their wedding, is portrayed in the movie as a scandal. As a matter of fact it is common for Orthodox Jews to dance with their brides on their wedding, this dance is called in Yiddish the Kosher-Tants. It is not prohibited for married men and women to dance with each other, although this does not apply to singles.
Incorrectly regarded as goofs: During a scene early in the second act, Tevye is seen with a pig in the barnyard. While Orthodox Jews do not raise or eat hogs, it appears Tevye was merely making a milk delivery. The barnyard probably belongs to a Gentile.