When Bogg and Jeffrey leave Rome in 44 B.C., a soldier is heard saying "Stop in the name of the Roman Empire." At the time of Julius Caesar's death, Rome was still a republic. It didn't become an empire until 27 B.C. and the coronation of Augustus.
Isaac Newton is depicted as having a beard. In reality, he never had one.
The Empire State Building can briefly be seen in the New York City skyline in 1927. However, its construction did not begin until 1929 and was not completed until 1931.
The 1927 Yankees were shown with numbers on their uniforms and Babe Ruth was introduced as "#3, Babe Ruth". The Yankees did not start putting numbers on their uniforms until the 1929 season.
A poster for City Lights (1931) is seen outside a cinema in New York City on May 21, 1927. However, the film was not released until January 30, 1931.
Jeffrey tells Bogg he'll teach him about curveballs, sliders, and screwballs, pitches that hadn't been invented in 1919, but Christy Matthewson had been using a screwball (called a fadaway) in the early 1910s and the curveball (or skewball) dates back to 1870. The slider seems to have come into use in 1920.