This serial certainly IS not historically correct. At the very beginning it has Jesse James saying he knew nothing about the Northfield Minnesota raid, whereas he was, in fact, the leader of the gang who perpetrated the raid.
In Chapter Two you can see a rope that's pulling the burning hay wagon.
Western gunslingers were traditionally very "monogamous" about their firearms (i.e., they strongly preferred not to use or retain other people's guns in favor of their own personal weapons that they were accustomed to using; think Billy The Kid in Howard Hughes' "The Outlaw"), so it is unlikely that Jesse would have casually holstered Jim Clark's oversize revolver instead of his own handgun in the film's final shot.