Continuity mistake: When Ness is "escorting" Nitti off the roof of the courthouse, watch the proximity of the two to the rooftop door. When the camera cuts from the edge of the roof to Nitti and Ness and then back to the edge of the roof, you can see that they went from close to the rooftop door to really far away from it.
Factual error: In the warehouse scene with the wooden crates with maple leaves, even though a correction has been submitted saying a maple leaf was valid, the real mistake is the type of maple leaf used. The film shows a modern graphic style of leaf that did not come into use until the 1960s and appeared on the new Canadian flag in 1965. In the time of Capone, the maple leaves used to depict things Canadian looked like actual maple leaves and not like a stylized graphic.