Continuity mistake: After Belle says good morning to Jean Potts, when she feeds the apple to the donkey note the rope (crosstie) is tied off at the donkey's throat, but in the next closeup the rope is tied off directly to the halter knot at its cheek.
Visible crew/equipment: While Barnum and Phillip sing "The Other Side" Phillip uses two stools to get up and down from the bar top. When he steps down from the bar top, in this wideshot (also the first shot of them in the pub and other shots) the two upright stools Phillip used are secured with additional support, note the floor area underneath the stools' legs have the same pattern as the rest of the floor, though we can see the outline where the pattern's lines don't match up. Additionally, we also see three actors' marks (in the shape of an "L") on the floor in front of the bar, which will be where Barnum and Phillip will stand when they agree on the ten percent. (00:36:05)