At 7:45, the position of the kids in the wagon change.
At 1:26:10, Gil's position on the house changes.
When singing around the organ, the three boys and Gretchen are clapping in time to the music. A close-up of Dion shows him clapping, but very slowly, not in beat. The next shot with all of them again has them all clapping in rhythm in beat.
Carrie Donohue's testimony is stricken because "the law says a wife cannot testify against her husband" and Dion O'Leary marries Belle Fawcett for the same reason. However, the law only says that a wife cannot be compelled to testify against her husband; she can still testify of her own free will.
Just before the fire in 1871, the Mayor speaks about replacing the combustible buildings in "The Patch" with newer ones made of stone and steel. The first buildings with steel frameworks were not constructed until the 1880's. Before then, large buildings were constructed of wood with a stone shell.
During the fight scene between the O'Leary brothers the smacking sound occurs a few seconds after the blow to the face.
During the fire scene with the crowds racing to the river in terror a woman can very briefly be seen laughing as she runs.