Mary recieves a telegram dated August 8, 1927. Later in the film, Jack is seen writing a letter to Mary, dating it August 7, 1927.
Jack and his mother rise from the piano twice upon the Cantor's entry.
In the scene where the Cantor prepares to whip the 13-year old Jakie, the boy has three buttons conspicuously pinned to his shirt for most of the take. However in the shot where the cantor shoves him towards the bedroom, there are only two buttons.
The head on Yudelson's beer disappears and re-appears between shots.
The handkerchief in Jack's suit pocket seems to change shape between shots in numerous scenes.
During the audience applause after "Tootsie", it's clear that the clip is just being looped, as a person behind the counter in the background repeatedly enters from off-screen without exiting.
When Jack is writing the aforementioned August 7 letter to Mary following the Yossele Rosenblatt recital, immediately after he writes the words "nearly stopped," there is a splice in the film (but not the soundtrack) and the insert of the writing is repeated at an earlier point so that Jack writes the same sentence again. This may have been to allow for a reel/disc change, since there is a conspicuous pause of silence in the middle of the shot where the music cue ends and another begins.
Jack's whistling "Toot-Toot-Tootsie" is clearly out of sync in the close-up.
Before Yudelson enters the Rabinowitzes' home, he touches his hand to the mezuzah and kisses it. However the mezuzah is on the left side of the door, instead of on the right where it's supposed to be.
When Jackie Rabinowitz instructs the band to play "Toot, Toot, Tootsie" he calls for it to be played in 3/4 time. The band then proceeds to play the song in 4/4 time.