Though the story takes place no later than 1910 (the year of Tolstoy's death) the map linking sequence between the Russia and Greece segments show frontiers established after the II Balkan War (1913). Bulgaria's shape in particular is pretty revealing.
Young Indy tells Tolstoy that Christy Mathewson had a record the previous year of 37-11 and reports his Earned Run Average (ERA) as having been 1.96. There are two problems with this. While Mathewson had a record of 37-11 in 1908 (placing the scene in Russia in 1909), his ERA in 1908 was 1.43, but it was calculated many years later, as the National League did not calculate or report ERAs until 1912.
Indy's baseball glove is a modern (i.e., late twentieth century) shaped baseball glove with firm leather and a stitched-together four fingers and a web linking the thumb. Baseball gloves in the early twentieth century were unshaped soft leather, giving the fielder better control of the soft glove.