In LSD's number "Love Power", his musical ensemble consists of a guitarist, keyboardist and sax player, however, the music we hear clearly has flute, bass guitar, drums and other instruments not represented, and no saxophone.
During the time in Liebkind's flat and leaving it Max and Leo are wearing Nazi bandages on the right arm. However the real swastika bandages were worn on the left arm. Since Franz Liebkind was a "true" Nazi, he should have known that.
When Max and Leo are about to enter Franz's apartment building, a pretty woman passes by and they check her out. In the distance, a young man exits another building; as the woman gets closer to him, they obviously don't know one another. When Max and Leo leave Franz and walk onto the same sidewalk in front of the building, the very same pretty woman can be seen walking towards them; what's more, she is with the same young man who was exiting the building, and now they are a "couple."
When Max and Leo are trying to talk Roger De Bris into directing "Spring Time for Hitler," Roger's personal assistant, Carmen Ghia places a wig on Roger's head to complete his costume for the choreographer's ball. As the scene cuts back and forth from wide shots to close ups of Roger while he is speaking, the bangs of his wig alternate between being off and on his forehead.
In the bar The Drunk is between Max and Leo as the patrons leave for the second act. After the shots of Max putting his head on the jukebox and Leo caressing his blanket when Max comes back to the bar, to calm Leo down, The Drunk has disappeared.
On opening night, the shots of people getting out of their cars show the Cort Theatre on the other side of the street. There is now no theatre across the street from the Cort but until 1969 it was Broadway's Playhouse Theater.
Leo claims in the bar scene that he went from a meaningless accountant one day to the producer of a broadway flop the next. The events of the film shown up to this point could not possibly have taken place in a single day, given that they had to find a flop play, Max had to go seduce several old women, and they had to go about getting the play director, stars for the play, holding rehearsals, and a crew assembling the setpieces for said play. There is simply no way this all fits into a single calendar day.
After Bialystock and Bloom enter Roger de Bris' house, Carmen Ghia immediately asks them to take off their shoes to keep the white carpet clean. While on a shot of their faces, we see them both take off their shoes and hear audio to that effect. Yet when they get into the small elevator immediately after and in s subsequent scenes with Roger de Bris, they are obviously wearing shoes.