The idea that Dr. Totenkopf, who has been dead for 20 years in the story, is being portrayed using re-cut archived footage of Laurence Olivier, who had died 15 years before the film is released. The idea of a dead man portraying a dead man just kinda seems to work.
In a minor case, Joe refers to "World War I." At the time the film is set, the sequel hadn't broken out. It would have been called "The Great War" (or "The World War", which was used at the time, although mostly by Germans).
Given the extent and severity of the robot attacks against cities and resources worldwide, it's entirely plausible that Joe and others consider that to constitute World War II in their Alternate History. Any global conflict that the Axis powers might subsequently stir up would have to be called World War III instead.