If you watch Burgundy shooting the gun while Brady and Cantrell are about to be hung, the magazine can be seen at different levels of capacity. There was continuous firing, however, Burgundy never reloads the gun.
The film is set during Theodore Roosevelt's tenure as President. That would have been between 1901 and 1909. It is stated that "Diamond" Jim Brady is promoting a big boxing match between "Gentleman" Jim Corbett and John L. Sullivan. Corbett fought Sullivan, but in 1892. The events depicted in the film happened in two entirely different eras.