Moody mentioned about Kagan that, "He's no John L. Sullivan." Sullivan didn't start boxing until 1878, it was established that it was 1876 in The Aftermath.
There is a preliminary bout in the 1865 flashback. Since boxing matches at the time weren't timed or limited as to rounds, and often lasted for hours, prize fights almost always featured just a single bout.
When Joe Kagan walks to the ring in the 1865 flashback, the fighters already in the ring are wearing modern-style boxing gloves. That they were wearing gloves at all for a professional fight would be very unlikely, with the Marquess of Queensberry rules not being written until 1867 or ubiquitous until the 1890s.